I support the effort if not the execution.
Since we're offering suggestions:
Having looked at the problem in some depth and having read several economists theories, it appears to me that the fundamental underlying causation of the issue is property values. Without a "bottom" to housing prices, the "unwinding" of highly leverage financial institutions will continue no matter what TARP does. In order to get to the bottom of the housing pricing trough, people have to have buying power (borrowing power) and the belief that real estate assets are priced at their value to stimulate sales and stop prices falling. Their in lies the rub.
Until something is done to stem the tide of foreclosures, nothing will prop up housing values and prices will continue to tumble causing more write-offs at banks, causing less lending, causing less spending, causing more lay-offs, causing less spending, etc. It is a never ending negative feedback loop pushing housing prices down.
In order to stop that cycle, it would seem prudent (not fair, but prudent) that the Fed step in and guarantee the distressed loans, but force the banks to refinance anyone with reasonable credit at 80% of the current depressed value of the house at a 30 year fixed rate, and guarantee the loan. This would dramatically reduce the number of foreclosures, the lender only has to write down the incremental value of the loan, not the whole thing, and the "value" of the home is effectively stabilized around the guaranteed loan value. Obviously this is not fair for those of us who are not is a position to need foreclosure assistance, and it effectively helps those who made risky decisions, but in the long run it stabilizes the rest of the market values and keeps people in their homes and with more money in their pocket, spending more, and that would stimulate economic growth. The trade off would be that if the fed forces a loan refinance for the distressed asset, the bank that wrote down the loan gets a stake in the equity of the home at the future sale to make up for the loss and so the homeowner doesn't unfairly gain if the value of the house goes up.
That is how I would spend $800B.