While Twitter may need Google to continue offering archive search, Google also potentially needs Twitter in another way. Google may have lost some of the data it has recently been using to bring social signals into its results, as covered more below:
Google’s Search Results Get More Social; Twitter As The New Facebook “Like”
I’ve not yet been able to check on whether Google Social Search and other parts of Google have been impacted by the deal’s end. I’ll look at that later — I’m heading off to enjoy the 4th Of July myself now.
Update: Google has sent us a statement addressing the issue above:
While we will not have access to this special feed from Twitter, information on Twitter that’s publicly available to our crawlers will still be searchable and discoverable on Google.
As for other features such as social search, they will continue to exist, though without Twitter data from the special feed.
You can certainly understand why Google+ has become even more important to the service now. While Google has gotten by largely without social signals from Facebook, having its own data from Google+ gives it insulation if it now has to get by without Twitter signals, as well.