By funneling $75 billion to people who might have otherwise foreclosed, the plan will keep their homes from going on sale at firesale prices. At least in the short term, this will prop up home prices. It will keep the paper value of peoples' wealth from dropping. And it will prop up the prices of some assets backed by mortgage debt.
All of this is assuming that $75 billion is enough money. It may be like spitting into the wind. Maybe it will buy some time. I'm guessing that it will "work" in the sense that I described above, at least for a time.
But what other consequences will it have? The $75 billion is a wealth transfer to mortgage payers. From whom will it come?
From the sounds of things, it will not be financed by taxes. Pelosi's stimulus bill is supposed to reduce taxes while raising spending. Most likely, it will come in the form of increased government borrowing. This new debt will compete with private capital. So leveraged companies may find it harder to find financing as the capital markets are squeezed dry. If companies go under because of the inability to find capital, the very people who, in the short run, were helped by the mortgage plan may be harmed by losing their jobs. That is, of course, unless Obama comes along with yet another intervention.
The other method of financing the $75 billion is through inflation. If the federal government issues debt and places it on reserve at the Federal Reserve, it will receive new currency with which it can pay the $75 billion. However, doing so will further devalue the dollar. While mortgage payments may be supressed, the price of other things would go up. Meanwhile, inflation never works uniformly on an economy. We would almost certainly see distortions in the price structure that would lead to further business failure. More interventions would be called for.
I hope that you see a pattern. Obama's mortgage plan is likely to have unintended, negative consequences. While it may succeed in its immediate goals, it will also cause other problems that could be worse than the initial problems. What's more, we could trace cause and effect back to prior interventions into the economy that caused the current mortgage crisis.
We should not imagine that no problems would ever be seen in an unfettered free market. Humans make mistakes. But the market, through profit and loss, has a mechanism to correct mistakes. Government is built to compound the mistakes because it lacks (at least until it entirely wrecks society) any concept of profits and loss. Government failure may always be met by increased funding. The unintended consequences of its policies are rarely adequately recognized. And they may always be followed by new policies.
In a broader sense, this does not "work" for me. We should fundamentally change our thinking of the role of government.