Simple, Elegant Solution to the Mortgage Crisis?

So far, throwing billions of dollars at major banks like Citigroup does not seem to be working.

This is because mortgages are continuing to default, causing the bank's mortgage backed derivatives to deteriorate further.

I wonder if we can't solve this problem elegantly, without spending any more money.

Why can't the government stop foreclosures by requiring the banks to rework mortgages with variable terms?

A variable-rate mortgage is where the rates change, depending on the interest rate.

Instead, why can't the banks work with individual homeowners and simply change the terms until they reduce the monthly payment to something the homeowner can afford?

For example, change the term from 30 years to 40, 50, 60. Heck, even go out to 100 year mortgages in some cases, if needed.

You could argue that the homeowner would not live long enough to pay off a 100 year mortgage, but the point is this would be a mathematical abstraction to keep the homeowner in the house, and stabilize the mortgages underlying the derivatives.

Chances are, these long term mortgages, like all mortgages, will end up getting paid off within 20 years when the owners refinance or move.