At heart, the problem is that people can't pay their mortgages, and no one can be found to come in and buy the houses when they foreclose, which means the securities can't get paid off.
One of the problems with buying those securities as a market stablization strategy is that no one knows what they're worth or what the risk involved in them is. Indeed, that's how we got to where we are right now.
My solution: Buy foreclosed or foreclosing houses. Houses are still being sold, so you can calculate a price, and there's a concrete asset that you get. The banks get some of their money, so that should get the securities moving.
The best part: you can remortgage the house to the previous owner on a different set of terms (i.e. the fixed rate, long term, variable payment model I saw and can't find the link to).
Note that my plan is basically ripped-off from the Center for American Progress's plan, except that they call for the financial companies to undo the securitization and put the mortgages back together before the government will buy them. I think that step will be 1. Hard and 2. Invites manipulations because it is hard. Also, houses are easier to price than mortgages (i think).
Paraphrased as a comment at mDubious