Tom Rice, a Republican from his state who had backed impeachment.

Last week’s breach of the Capitol appears to have presented that opportunity to Republicans who want to refocus the party around Mr. Trump’s policies, and dispense with the polarizing language and divisive actions that marked his four years in office.

No, Trump does not have any blame, but the Democrats certainly do, along with all the Republicans that follow with them,” said Billy Long, the Republican Party chairman in Bayfield County, Wis., who said he was planning to break away from the G.O.P. to start a local Trump-centric third party. “The Trump movement is not over; like Trump said himself, we are just getting started.”

Republican voters, too, have largely drawn a sharp distinction between the president and those who stormed the Capitol, with 80 percent saying they do not hold Mr. Trump responsible for the rioting and 73 percent saying he is protecting democracy, according to polling released by Quinnipiac University this week

Even if Mr. Trump fades from political life, losing his social media megaphone and bully pulpit, his supporters say his message will be carried forward by a party remade in his image and with strong structural support at all levels.

“The election was crooked and Republicans who could have done something did very little,” said Dave Wesener, the chairman of the Republican Party in Crawford County, Wis. “Those Republicans who have not been supportive I affectionately call RINOs. All RINOs should be primaried by conservatives.”

The siege at the Capitol last week has drawn an even brighter line dividing the party. State legislators from more than a dozen states attended the protest, with at least one facing criminal charges for breaching the Capitol as part of the riot. Meshawn Maddock, an activist who is poised to be the incoming Michigan Republican Party co-chairwoman, helped organize busloads of supporters from her state to travel to the Capitol. In the days after the violence, she joined a conservative online group where some participants openly discussed civil war and martial law.

Chinese internet companies conduct their own censorship, but they do so out of fear of what Beijing officials might do to them. Last February, ifeng.com, a news portal, was punished for running original content about the coronavirus outbreak. Under the Chinese regulations, these websites can’t produce original news content.

For those reasons, many Chinese are dumbfounded by the idea that private companies such as Twitter and Facebook have the power to reject a sitting American president.

But when Mr. Kuang created two cartoons to express his displeasure at Mr. Trump’s bans, China’s censors did nothing. In one of them, President Trump’s mouth was brutally sewn up. In another, the Facebook founder Mark Zuckerberg is portrayed as Qin Shi Huang, China’s first emperor, a brutal tyrant who burned books and executed scholars more than 2,000 years ago.

The journalist Zhao Jing, who goes by the name Michael Anti, is puzzled why Chinese Trump supporters so zealously defend his freedom of speech. Mr. Trump has the White House, executive orders and Fox News, he wrote: “What else do you want for him to have freedom of speech?”

A retired firefighter from Chester, Pa., was also arrested on Thursday after he was identified as the man seen in a video throwing a fire extinguisher at police officers during the riot. The man, Robert Sanford, is charged with assaulting a law enforcement officer engaged in the performance of official duties and civil disorder among other crimes.

Another man was charged on Thursday after law enforcement officials identified him as the person seen repeatedly striking an officer with a flagpole on the stairs of the Capitol in a video posted on Twitter. That man, Peter Stager of Arkansas, was charged with obstructing law enforcement, according to the criminal complaint.

The answer also matters on a deeper institutional level. Some justices have drifted quite far from their ideological starting points. Harry Blackmun, John Paul Stevens and David Souter come to mind. All were Republican-appointed justices (by Presidents Richard Nixon, Gerald Ford and George H.W. Bush, respectively) who ended their careers as among the most liberal members of the court they served on. Could history repeat itself with any members of the Roberts court?

But Article I, Section 3 says more. In describing the powers of the Senate to conduct an impeachment trial, it provides that “Judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States” (emphasis added).

The Belknap case cemented two precedents: Congress can impeach and remove former officers, but the fact that the defendant is no longer in office is one factor that senators may take into account in deciding whether to vote to convict. So, when President Richard Nixon resigned in August 1974 in an effort to forestall his seemingly inevitable impeachment and removal, that act did not deprive Congress of the constitutional power to still impeach, remove and disqualify him; it merely mitigated the perceived political expediency of doing so. By resigning, Mr. Nixon took at least some responsibility for his conduct. And the circumstances of his resignation left no reason to believe that he would ever again be a candidate for federal office.

President Trump announced Friday that he would not attend Mr. Biden’s inauguration.

The F.B.I. and Secret Service have ramped up security efforts around the inauguration.

George W. Bush, has confirmed he would travel to Washington for Inauguration Day, along with Laura Bush, the former first lady. Barack Obama and Bill Clinton are also expected to attend, along with former first ladies Michelle Obama and Hillary Clinton. Jimmy Carter, who at 96 is the oldest living former president, announced that he and his wife would not attend. It will be the first presidential inauguration Mr. Carter has missed since he was sworn in.

The 20th Amendment to the Constitution requires that the term of each elected president and vice president begin at noon Jan. 20 of the year after the election.

Symbolically, it marks the peaceful transfer of power from the current president to the next. Inauguration Day will be all the more important this year, as Mr. Biden ascends to the presidency at a time when political division has threatened the nation’s democratic institutions and his predecessor has gone to extreme lengths to stay in power.

The Moderna vaccine is a particularly attractive candidate for rapid scaling, since it can be kept at normal freezer and refrigerator temperatures, which makes it easier to store and transport.

After all, viruses know no borders. Protecting Americans from Covid-19 requires protecting all people from the disease. We will not end the pandemic until everyone, across the world, can receive highly effective vaccines. And the U.S. can help the world more quickly this time. Pepfar was launched seven years after effective H.I.V. treatments were available in rich countries.

Representative John Katko of New York was the first Republican to publicly announce that he would back the impeachment proceedings.

Representative Liz Cheney of Wyoming, the No. 3 House Republican, said on Tuesday evening that she would vote to impeach, citing the president’s role in an insurrection that caused “death and destruction in the most sacred space in our Republic.”

Representative Adam Kinzinger of Illinois, a frequent critic of Mr. Trump, joined his Republican colleagues on Tuesday evening, saying the nation was in uncharted waters. He said that Mr. Trump “encouraged an angry mob to storm the United States Capitol to stop the counting of electoral votes.”

“There is no doubt in my mind that the president of the United States broke his oath of office and incited this insurrection,” he said

Representative Fred Upton of Michigan issued a statement saying that he would vote to impeach after President Trump “expressed no regrets” for what had happened at the Capitol.

Representative Jaime Herrera Beutler of Washington State said that she would vote to impeach because she believed that the president had acted in violation of his oath of office.

A sixth Republican, Representative Dan Newhouse of Washington State, announced his plans to vote for impeachment during a debate on the topic in the House on Wednesday.

Mr. Newhouse said that others, “including myself, are responsible for not speaking out sooner — before the president misinformed and inflamed a violent mob.”

What he concluded, he said, was that President Trump “helped organize and incite a mob that attacked the United States Congress in an attempt to prevent us from completing our solemn duties as prescribed by the Constitution.”

Representative Peter Meijer, a freshman congressman from Michigan, said in a statement that the president had “betrayed and misled millions with claims of a ‘stolen election’” and that during the riot at the Capitol he “shrank from leadership when the country needed it most

In a statement, Mr. Rice had a blunt critique of President Trump. “I have backed this President through thick and thin for four years,” he said. “I campaigned for him and voted for him twice. But, this utter failure is inexcusable.”

After casting his vote to impeach, Representative David Valadao of California said on Twitter that “President Trump was, without question, a driving force in the catastrophic events” that took place at the Capitol.

The federal officials also wrote that “the shared false narrative of a ‘stolen’ election,” the false claim perpetuated by President Trump, “may lead some individuals to adopt the belief that there is no political solution to address their grievances and violent action is necessary.”

The Boogaloos marked themselves by wearing their signature Hawaiian shirts. A group of Proud Boys showed up in orange hats.

Alongside the violent, the overtly racist and the paranoid were thousands of devoted Trump supporters, some of whom even brought young children. The crowd was filled with people in MAGA regalia, and Trump flags were everywhere. Most just said “Trump”; others were a bit more outlandish.

While his unwavering support from about a third of the electorate has saved Mr. Trump from dipping into the 20s, where Richard M. Nixon and George W. Bush both were near the end of their presidencies, the latest numbers reflect his diminished support across the board, including among Republicans; his job approval among members of his own party, once almost universal, has dipped into the 70s.

“I made it like a foot inside and they pushed me out and they maced me!” she cries. When Walker asks her why she wanted to go in, she’s exasperated at his ignorance. “We’re storming the Capitol, it’s a revolution!”

But even after seeing his friend walked on by Trump’s supporters, Winchell could not see how Trump was to blame. He was shocked when the TV reporter asked him if the president “has blood on his hands.”

The Senate’s majority leader, Mitch McConnell, has said that he cannot commence an impeachment trial before Jan. 20, unless all members of the Senate agree to allow it sooner. In fact, as Chuck Schumer, the minority leader, has suggested, in emergency situations, the rules allow him and Mr. McConnell to reconvene the Senate immediately. Removing from power at once a president who has incited an attack on his own government certainly qualifies as an emergency situation.

We should not allow that to happen. He tried to steal the election and incited a mob to abet his wrongdoing. He is a danger to the nation and must be removed immediately and disqualified from ever holding public office again.

Just hours after rioters were cleared from the Capitol on Wednesday, there was already discussion about what would happen next on Parler and Gab, another social-media platform that has become popular with the far right.

Andrew Torba, chief executive of Gab, said: “As we have communicated to our partners in law enforcement, we have adopted a heightened security posture in the lead-up to the inauguration and are ready to respond quickly to any request law enforcement may make of us during the period.”

Kevin D. Greeson, 55, of Athens, Ala., was standing in a throng of fellow Trump loyalists on the west side of the Capitol when he suffered a heart attack and fell to the sidewalk. He was talking on the phone with his wife at the time.

Rosanne Boyland, 34, of Kennesaw, Ga., posted fervently in support of President Trump on social media, followed the baseless conspiracy theories of QAnon and latched onto Mr. Trump’s false claims that he had won the election, family members told The Associated Press.

How she died remained unclear on Monday

Mr. Philips died of a stroke in Washington, those who accompanied him to the Capitol told the newspaper. The exact circumstances of his death were still unclear, and his family could not be reached for comment.

Then, after it was clear Mr. Biden was the victor, and after weeks of public and private attempts to get states to change their vote totals and deliver him a second term, the president encouraged his supporters to converge on Washington on Jan. 6. (“Be there, will be wild!” he tweeted.) Tens of thousands of them, from all over the country, answered his call.

If Republican senators refuse to convict Mr. Trump, they would go on the record — for their constituents to see and reconcile — defending a man who was happy to put their lives, and the nation’s democratic future, at risk for nothing but his own quest to hold on to power.

Mr. Trump is not the only person at fault. Many Republican lawmakers riled up his supporters for weeks with false claims of election rigging and continued to object to the electoral vote even after the attack. The 14th Amendment bars from office any federal or state lawmaker who has “engaged in insurrection or rebellion” or given “aid or comfort” to those who have. Congressional leaders will need to reckon with which of their colleagues require censure for their actions, and perhaps even expulsion.

About 6,000 National Guard troops from six states have already arrived in Washington, Gen. Daniel Hokanson, the chief of the National Guard Bureau, said Monday; by this weekend, that number is expected to have grown to 10,000.

The officials said they were particularly worried about multiple active-shooter situations flaring up simultaneously.

Far-right extremist groups continue to plot online. Nearly 400 people had joined a private group online dedicated to what is being billed as the Million Militia March, an event scheduled to take place in Washington on Jan. 20. Commenters have debated bringing baseball bats and body armor.

General Hokanson pushed back against complaints from Gov. Larry Hogan, Republican of Maryland, that the Pentagon was slow to respond to his request that Maryland National Guard troops be deployed last Wednesday.

General Hokanson insisted that Defense Department officials responded to the Hogan request Wednesday afternoon, and the first of the Maryland troops were not ready until 11 p.m. that day, with the bulk of them not deployed until 9 the next morning.

We were escorted back to the Senate chamber, swept free of broken glass, and resumed our certification of the electoral votes. We held fast to the oath we swore to support and defend the Constitution of the United States against all enemies, foreign and domestic.

It is our job as senators to represent the will of the American people. That meant making it clear that while this riot was a temporary disruption of the democratic process, it was not a disruption of our democracy. So, after the violence came to an end, we set out to fulfill our constitutional duty.

Unlike the peaceful protesters who gathered in Lafayette Square or across New York City last year for Black Lives Matter protests, the rioters at the Capitol were not met with overwhelming police and military force.

They were not stopped from storming onto the Senate floor, taking a podium or defacing the speaker’s office. We should all consider what that says about our country, how we see public safety and racial biases in our law enforcement.

Every option available, from invoking the 25th Amendment to impeachment and removal to criminal prosecution, should be on the table.

Congress and the Department of Justice must undertake a thorough investigation of how this happened, and why the planning for this protest and response to these white supremacist groups was so inadequate, putting lawmakers and the people who work in and maintain our Capitol building at risk. More broadly, we must assess the role of the ultra conservative media, which purports to be news but only offers misinformation and division, as well as the power of unchecked social media to divide our nation

“We believe the risks of allowing the president to continue to use our service during this period are simply too great,” Mr. Zuckerberg wrote.

Lawmakers and even employees of the companies said the platforms had waited too long to take serious action against Mr. Trump.

Jack Dorsey, Twitter’s chief executive, spent Thursday morning liking and retweeting commentary that urged caution against a permanent ban of Mr. Trump. That suggested he would not deviate from the plan to allow Mr. Trump back onto the service.

At Facebook, that unwillingness changed on Wednesday after Mr. Trump egged on his supporters using social media and a mob stormed the Capitol building.

After Twitter locked Mr. Trump’s account late Wednesday, Mr. Zuckerberg approved removing two posts from the president’s Facebook page, the two people said. By that evening, Mr. Zuckerberg had decided to restrict Mr. Trump’s Facebook account for the rest of his term — and perhaps indefinitely, they said.

The social media companies’ clampdown extended beyond Mr. Trump. Twitter overnight permanently suspended Lin Wood, a lawyer who had used his account to promote the conspiracy theory QAnon and to urge on Wednesday’s mob. The company also removed a post from Dan Bongino, a conservative podcast host, on Thursday.