I would like to search Twitter messages containing a given search term, but in the relatively distant past (one week), potentially with the specification of a timeframe where the search is performed.
Is it possible?
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Take a look at Topsy.com
Use the "until" option, on the search form at search.twitter.com or through the API: http://apiwiki.twitter.com/Twitter-Search-API-Method:-search
You could try Snap Bird by Remy Sharp. It can search much further back in time than normal Twitter searches.
Searchtastic seems to search pretty far back, although I don't believe you can specify timeframe. I've had good success with it.
Not sure how it would work for you, but something to check out.
I also found this link comparing Twitter search sites. http://mashable.com/2009/04/22/twitter-search-services/