Do not agree to a deed in lieu without consulting an attorney. The devil is in the details and unless you are able to make sense of the terms and conditions, you may be waiving your some of your rights. I have seen some built in with promissory notes for the unpaid loan balances. Good Luck!
Pam - you should really consult with a real estate attorney to confirm this. Every circumstance can be different and Larry is correct we do have the anit-deficiency law and it is primarily on purchase money primary property but not investment type or re-fi. However, Realtors are not and should not qualify their answers as certain as we must function in our expertise and refer where appropriate. This is one of those cases. If you'd like some names of attorneys to contact then let me know. If you would like to consider a short sale our office has a short sale group that handles them specifically.
In Arizona there is an anti-deficency law that prevents lenders from being granted judgements against you on your home. This would only apply if it where a commercial property. Do be aware though that this only applies to deeds of trust. If you have a "Line of credit" there may be a liability to repay that debt.
Check with a attorney but when a mortgage company accepts a deed in lieu there should be no deficeincy judgment. But I have seen some banks to some strange stuff in the last 6 months, so confirm with the bank.