Tracphone is the company you want for this sort of thing. A SIM costs $0.99 (requires unlocked phone of course) and you add $15 to the account to get 500 texts. (I think you can do this with cash at a place like Walmart.)
It is expensive if you need to keep the plan around, but Twitter doesn't seem to regularly send SMSes to the phone number, so you probably don't need to pay beyond the first month.
It is expensive if you need to keep the plan around, but Twitter doesn't seem to regularly send SMSes to the phone number, so you probably don't need to pay beyond the first month.