The idea of the insurance plan, championed by Representative Eric Cantor of Virginia, was to reduce uncertainty and restore confidence without actually using taxpayer money.

The federal government would guarantee the underlying mortgages in a mortgage-backed security, much as Fannie Mae and Freddie Mac have done for years and as the Federal Housing Administration does, as well.

In theory, the cost of that insurance would be borne by the companies that hold the mortgages or mortgage-backed securities.

Treasury officials had already told Republican lawmakers they had considered an insurance approach, but rejected it. The problem, from Mr. Paulson’s standpoint, was that insuring against mortgage defaults would do little to increase liquidity, or the amount of money available for making loans. By contrast, the Treasury plan would inject hundreds of billions of dollars in fresh, although borrowed, money into the marketplace.

But the insurance plan could pose other risks to taxpayers. The government would be insuring the riskiest and most default-prone mortgages made during the housing bubble, including loans that required no down payment and no income verification by the borrowers.

The allure of insuring mortgages, rather than buying them as Mr. Paulson would, is that the government would not have to put up any taxpayer money. But because the government would be guaranteeing nearly all mortgages in the country, since it already owns Fannie Mae and Freddie Mac, taxpayers could face big losses if losses from defaults turn out to be higher than expected.

Many House Republicans, including Mr. Ryan, had come up with a far more detailed rival plan earlier in the week that included Republican policy evergreens like new tax breaks and more flexible regulation as well as the insurance idea.