Can a bank forclose on your home if you make a partial payment?

My bank screwed up my escrow account and increased my monthly mortgage payment by over $250 a month. I have been working with them for almost 6 months to fix this or at least help me with a payment plan. They keep putting me off or ignoring me. I did get turned down (not qualified) for the governement relief programs that are offered through my bank. I have even tried to re-fi . . . the valuations in my neighborhood have dropped to low!
I now have no choice but to start making partial payments. I know that this will reflect neg. on the credit report, but I have NO choice. What would the bank do to me -legally?