Your best bet, to really understand your options, is probably to speak with a real estate expert, mortgage broker, or attorney.
I don't have experience with the US Govt. Relief Program, but I would think the bank would want to do anything possible to avoid taking possession of your loan and your house.
There are a lot of companies out there who don't have your best interest in mind which is why I'd personally seek the advice of someone who could provide a little more understanding of the situation and work to help you find the best resolution.
Good luck! I hope you are able to resolve everything quickly.