Yours is a difficult situation, but not impossible. Robert McGuire's suggestion below sounds like an excellent place to start, especially since they have experience with helping people in similar circumstances.
Be careful if you're checking out Craigslist. There are a lot of rental scams on that site, and your circumstances could actually open you up to those sort of scam because they know you have limited options. Most of the scams will have rental rates, and/or deposit requirements, that seem to good to be true. That's because they are. They usually tell some story about doing mission work out of the country, or taking care of a sick friend or relative. The scam usually involves having you wire money or sending a money order out of state. If you call on one of those, and share your story with them, and they ask you to send money out of state, don't do it. It's a scam.
I also agree with Ron below, in that your best bet will be up front with people right away. Decent people will respect you situation, even if they can't help. And those that can, are more likely to, if you're honest with them about your circumstances.
You may also want to consider working with a property management company. It won't cost you any more, and they can vet options for you. That might save you time and frustrations.
I wish you the best of luck, and hope you find your new home soon.