Is it legal for a company to refuse partial payments? Do they have to the right to say we’re not going to help set up a payment schedule now, but we’ll be there to nail you later when you skip more than 2 payments! What am I to do?
Yes. Unless state law or your loan docs states otherwise they have no obligation to accept modifications to the terms and conditions of the loan.
I can’t offer any helpful advice, I’m afraid, but the answer to the first part of your question is that the mortgage company isn’t obligated to do anything that isn’t specified in the note that both of you signed, which amounts to a legal contract. If they want to be hard-asses, and stick to the terms of that note, that’s their legal right.
Usually, mortgage companies aren’t eager to foreclose on a mortgage, since they don’t really want to be in the real estate business, but if the housing market is strong, they figure there’s no reason to try to accommodate you. They’ll be perfectly happy to foreclose, sell the house, and walk away with their money. 
God, I hate saying this…
See a lawyer. State laws vary greatly re. residence foreclosure, steps they must take, etc.
No, you can’t make them accept partial payments (unless your state says they have to) - your mortgage document undoubtly spells out their right to payments per schedule, and, as you have noticed, they can be quite nasty about it.
If worse comes to worse, you can go chap 11 and maybe buy some time from the court process - upon filing, all creditors are frozen (unless the GOP has gotten its way) until the court decides what money goes where. Again, see a lawyer
I think that Bankruptcy Chapter 13 let’s you keep the house – it also requires continuing payments to certain lender (IIRC), so does not “wipe the slate” like Chapter 11.
They are pricks and no, you cannot offer partial payments…however, most offer a payment plan option.
Take it and stick with it. Sell your car, sell your jewellry, sell whatever you got. Get back on terms and then, if you don’t think you can keep up, sell your house…fast.
Mortgages are not like your old landlord…you can’t promise to pay and throw a few bucks. These companies are run by computer. The calls are generated by computer when you are late, and the computer generates default…meaning you are gonna be screwed BIG TIME if you do not pay. I am SO serious…call them back…make a payment arrangement…it will be high and ridiculous…but like I said…
Sell your car, sell your jewellry, sell grandma…if you don’t, you are gonna be screwed big time. Sorry to be the bearer of bad news on this holiday season.
It is true that bankrupty proceedings stop any foreclosure. But don’t even think about doing that yourself. Get a lawyer, fast. Most will take payments on a monthly plan…who’da thunk.
Trust me…if you are at this point, you really don’t have any time to lose. Go. Do it now…call. Very serious.
Not only is it legal, but in most states, if you don’t make the agreed upon payment, the company can demand payment in full.
Then foreclosure starts.
Do whatever you have to do. If you have enough equity in the house, consider refinancing. Now is a good time, as interest rates are very low.
If you are old enough & you own your house, you can ask your bank for a ‘reverse Mortgage’. Yep, then the bank pays YOU money 
Otherwise I agree with the others, it depends on your contract, which we don’t know about.
Reverse mortgages are extremely unusual, and useful only if you don’t think you’re going to be around for more than a couple more years. I doubt a reverse mortgage would be useful to you, Jinx.