The Library of Congress expects to finish with their Twitter archiving project by the end of this month. So far, the archive contains about 170,000 tweets. But it will remain inaccessible for the foreseeable future, because it’s too huge to search:
The Library has not yet provided researchers access to the archive. Currently, executing a single search of just the fixed 2006-2010 archive on the Library’s systems could take 24 hours. This is an inadequate situation in which to begin offering access to researchers, as it so severely limits the number of possible searches.