The API says this is optional
q: Optional. The text to search for. See the example queries section for examples of the syntax supported in this parameter
e.g
http://search.twitter.com/search.json?&q=twitter[
^]
So try just with the since parameter
http://search.twitter.com/search.atom?since=2010-02-28[
^]
This will undoubtedly fail though because as Alison has pointed out, it's a very large amount of data to return over the wire. Twitter probably have some resource limit \ timeout options otherwise people running these sort of queries would constantly bring the site down.
You going to have to think about how to buffer the data and retrieve in chunks by using a combination of parameters
Possibly
since_id and
max_id are best bet, e.g
Chunk 1
http://search.twitter.com/search.atom?since_id=1520000000&max_id=1520100000
Chunk 2
http://search.twitter.com/search.atom?since_id=1520100000&max_id=1520200000
etc etc
Even retrieving small data using lots of requests, you're going to chew up bandwidth & I wouldn't be surprised if you find your IP being blacklisted! Don't know what you could possibly want with 50m inane comments about 'brushing my teeth' and 'about to have breakfast'