Under the Republican plan, instead of the having the government buy bad mortgage debt, investors such as banks and financial firms would pay premiums to the US treasury to finance insurance coverage.
The idea is that the insurance would give investors enough confidence to buy the illiquid securities and establish a market for them.
John Boehner, the House Republican leader, says the Republican alternative would also involve a smaller role for government.
The house Republican plan would also:
Offer temporary tax relief to free up capital for companies to lend to one another
Temporarily suspend dividend payments by financial institutions
Require participating firms to disclose to the US treasury the value of mortgage assets on their books, private bids on them in the past year and their last audit reports
Forbid government-sponsored mortgage giants Fannie Mae and Freddie Mac from issuing securities on unsound mortgages
Require the Securities and Exchange Commission to investigate the performance of credit rating agencies.
But Robert Litan, an expert on banking and finance at the Brookings Institution, called the framework unworkable, saying it would not achieve the basic goal of creating a market and establishing prices for mortgage securities that no one is willing to buy.
Eric Cantor, a Republican congressman, said the plan would be to remove the burden of the bail-out from taxpayers and instead place it, over time, on Wall Street itself.
"Instead of a purchase scenario, where you have the government injecting $700bn right up front into the markets, what you have here is an insurance plan," Cantor told reporters.
"In order to get this insurance, the banks with these failed assets would have to pay for the government backing, pay for the insurance."
Nancy Pelosi, the Democratic speaker of the house, said Paulson should decide the fate of the surprise Republican alternative.
"If it is something that can be included in the bill in terms of the authority given to the secretary, I would hope that that could be worked out," Pelosi told reporters. "If it is contradictory to the purposes of the legislation, then it is up to the secretary to decide."