I'm sorry for your situation. You are in good company with many people in the current economic tough times. Before you give up, please consider all of your options and make an informed decision while you have options available. Some of your options include, but are not limited to a Short Sale, Bankruptcy (which can extend your time in the home and perhaps allow you to recover) deed in lieu of foreclosure and outright foreclosure.
There are attorneys who can better advise you of the consequences associated with each choice. If you are financially unable to afford one, seek the state bar association for someone who can help for free.
To answer your question directly, each landlord will determine what level or credit worthiness is acceptable to them. Because so many people have gone through what you may be, there are some that are more flexible than others. You may find that writing a letter explaining your difficulties to submit with your application may be useful in improving your odds. Best of luck.