Never take the first offer. My client just received a very bullying "cash for keys offer" that told him to move out within 30 days and they'd give him $1500. I negotiated $3000 (their security deposit and prepaids from the deadbeat landlord that let the house foreclose).
Remember - banks are there to make money. Don't let them take advantage of you! When in doubt, talk to an expert and find out your rights.