If they can afford $700 billion to buy the banks' debt, they can certainly afford less than that to make mortgages not fail. The total cost of making most mortages not fail is less than the lost value on the bad debt. I was absolutely NOT looking at just "to pay this month" - that's utterly ridiculous. The TOTAL has to, by definition, be less, because otherwise it wouldn't cost that much to deal with the bad debt.
At worst, for example, the government could put in enough money to buy the house at current market value, losing whatever the difference was from its former value. That's not the best solution, but it is the limit of how much it should cost. If someone can continue to make payments for that much house value, they can continue to make payments, putting the right percentage of those into interest to make it at least break even. If they can't, they can "sell" and break even that way.
no subject
At worst, for example, the government could put in enough money to buy the house at current market value, losing whatever the difference was from its former value. That's not the best solution, but it is the limit of how much it should cost. If someone can continue to make payments for that much house value, they can continue to make payments, putting the right percentage of those into interest to make it at least break even. If they can't, they can "sell" and break even that way.