In essence, the administration has asked Congress for the temporary authority to provide emergency capital to Fannie Mae and Freddie Mac, either through direct loans or by buying stock in the companies, which are government-chartered but privately owned.
Paulson has said such aid is not needed now, and may never be necessary, but that the authority to step in is needed to reassure jittery investors.
Together, the companies hold or guarantee about 70% of American homeowners' mortgages.
It was clear after the meeting that Paulson has more work to do to win over Republicans.
"Some are concerned about an open-checkbook liability to the taxpayers," said Rep. John Campbell, a Newport Beach Republican.
He said Paulson sought to assure Republicans that "if this works, the markets will have confidence that it will really take care of itself, and the government backstop will make it such that the government doesn't actually have to ever step in."
Rep. Jeff Flake (R-Ariz.) said the reaction to Paulson was mixed.
"Everybody knows that something has to be done. It's just what are we willing to accept along with this, or what reforms do we get?"
The Republican rebellion reflects a long-standing strain between the party's conservative and moderate wings. Conservatives have never been happy with the two companies' hybrid status, especially what has almost universally been seen as an implicit government guarantee that Freddie and Fannie will never be allowed to fail.
The two "government-sponsored enterprises," as they are officially known, have been able to operate under lower capital requirements than other financial institutions, in large part because their mortgages -- which conform to strict underwriting and are capped at moderate levels -- were seen as safe bets for investors.
In recent days, however, investors began to worry that too many of the mortgages might go sour as the housing crisis deepened and home prices continued to skid.
They began selling off shares last week in what at least some members of Congress consider an unjustified crisis of confidence.
In testimony Wednesday, Federal Reserve Chairman Ben S. Bernanke agreed with that view. He told the House Financial Services Committee that Fannie Mae and Freddie Mac were "adequately capitalized. They are in no danger of failing."
"However, the weakness in market confidence is having real effects as their stock prices fall, and it's difficult for them to raise capital," he added.
