Aimed at propping up the housing market and helping strapped borrowers stay in their homes, the bill would also tighten the oversight of Fannie Mae and Freddie Mac, the mortgage giants that saw their stocks plunge this week.

"I would hope that people would see the bill as a confidence booster," said Frank, the legislation’s main House author and chairman of the Financial Services Committee.

Citing assurances that Treasury Secretary Henry Paulson made Thursday before his panel, Frank said that Fannie and Freddie, which benefit from an implicit government backing, were "well-capitalized."

A spokesman for Senate Banking Committee ranking member Richard Shelby (R-Ala.), Jonathan Graffeo, said that the House and Senate should move “immediately” to strengthen the regulator of Fannie and Freddie, known as the government-sponsored entities (GSEs).

"The first and most important step Congress must take is to move expeditiously to put a stronger GSE regulator in place,” he said, adding that Shelby has been in contact with the administration regarding Fannie and Freddie’s current situation.

The Senate concluded its work on the package Thursday evening, but the White House has threatened to veto the measure and it is certain to be modified in the House, perhaps as soon as next week.

The legislation, passed in some form by both the House and Senate, would allow for the refinancing of up to $300 billion in troubled mortgages into more stable loans backed by the government.

 In addition to tightening the reins on Fannie and Freddie, both the House and Senate versions contain a package of tax breaks intended to aid the housing market.

One of the biggest remaining sticking points is a measure granting $4 billion in block grants to states and towns to rehabilitate foreclosed properties.

The provision has divided House Democrats, with factions disagreeing over whether it should be offset to prevent it from widening the budget gap. Meanwhile, the White House has voiced strong opposition to the measure, saying it won't help people stay in their homes.

Frank said that he favored stripping the measure from the bill because he believes it is the biggest obstacle to gaining White House support.

He surmised that without the measure, the White House would sign the bill. "My hope is what we send them, they will accept," he said.

Frank said he supports attaching the block grant funds to other legislation and suggested that they be offset with an increase in the fees that securitizers pay to Fannie Mae when they bundle mortgages.

The idea had "great logic," Frank argued, because "if people hadn’t securitized bad loans, we wouldn’t have all this foreclosed property.”

Frank also raised concerns about Senate language to revamp the regulation of Fannie Mae and Freddie Mac. Under the Senate bill, the overhaul would need to be completed within six months.

Frank argued an immediate effective date would "cause chaos." He said he would push for a six-month delay before the new regulator could start promulgating regulations.

The House and Senate versions also diverge sharply on the size of mortgage Fannie Mae and Freddie Mac can buy. The House legislation would raise the limit from $417,000 to nearly $730,000, while the Senate bill would raise the cap to $550,000.

Finally, Frank also said that the affordable housing goals set forth in the legislation for Fannie and Freddie were “too cluttered” and needed to be simplified.