As I understand it, the GOP proposal is that instead of getting an equity share in the companies that have bad debt, we simply insure those bad debts. The distressed company holding a troubled mortgage-based asset gets a taxpayer-funded insurance policy for the full value of the asset in exchange for a small premium payment.
Of course, this is exactly what the mega-insurer AIG did, and look what happened to them.
All in all, it means that if these distressed companies get back on their feet, the taxpayer does not benefit from the upside (although the companies will). And if the distressed companies fail, then "we" have to pay the insurance, which will be astronomical, and so we suffer the downside.
Makes no sense, but perhaps I am missing something.