...senior House Republican... proposed that the government (presumably through the entity envisioned by the Paulson plan) offer to sell insurance to financial institutions that hold mortgage-backed securities (hereinafter MBS). Premiums would be determined by the rates of foreclosure on each class of securities so far. Under this plan, the government would be taking in money, not paying it out. Of course, if the premiums are not enough to cover losses, the government might eventually take losses, as it did when the savings and loan industry collapsed. But losses don't seem inevitable and in any case will mostly occur in out-years, not now.
I believe these mortgage backed securites are already insured. They were insured by AIG. The reason that the federal government had to take over AIG was because the fear that AIG would not be able to meet its obligation to cover those insurance payouts related to mortgage backed securities. So, in essence, the federal government is already doing what is being proposed.
AIG got involved in a new aspect of the financial system: It joined in the selling of so-called credit default swaps. A credit default swap, or CDS, is essentially insurance on debt.