Nervously eyeing the markets' next trading session, key lawmakers in both parties and Treasury Secretary Henry Paulson worked late into the night Saturday trying to close an agreement on a multibillion-dollar government bailout of distressed financial companies.

House Speaker Nancy Pelosi, D-Calif., told reporters "quite a bit" of progress was being made on a deal that Congress could send to President Bush as early as Monday after votes in both houses.

A key sticking point was how to include a new government-sponsored program demanded by House Republicans as an alternative to devoting the entire $700 billion proposed by Bush on buying up devalued mortgage-backed securities and other toxic debt from banks and investors.

"We're making a lot of headway; I think it's possible to get this thing done tonight," said Senate Finance Committee Chairman Max Baucus, D-Mont. "I can't guarantee it," Baucus quickly added.

"It is still a long way from completing it but we've made significant progress," Senate Majority Leader Harry Reid said.

Principal negotiators met with Paulson late Saturday afternoon, but according to one GOP source the meeting was very heated.

The source said House Democrats were calling for a new tax on securities firms, and that New York Sen. Charles Schumer told lawmakers he was concerned they were spinning their wheels. The source said Montana Sen. Max Baucus was also yelling at Paulson over executive compensation.

The meeting came after House Republicans said there was no deal yet, voicing lingering concerns about whether the legislation would adequately protect taxpayers.

β€œIt's important that we move, but it's important we move with discretion," House Minority Leader John Boehner said. "There are a lot of issues still on the table."

But after negotiations over the $700 billion bailout seemed to break down late Thursday, President Bush and senior leaders on Capitol Hill nevertheless expressed optimism they were nearing an accord.

"There is a widespread feeling we've made progress," Senate Minority Leader Mitch McConnell said Saturday.

In a positive sign, lawmakers called a meeting of the House rules committee, which is one of the first hurdles a bill must go through to reach the floor.

House sources said, too, they are hopeful a deal can be reached within 24 hours.

"Members of Congress from both sides of the aisle have contributed constructive proposals that have improved this plan," Bush said in his weekly radio address Saturday. "Republicans and Democrats must continue to address it together. And I am confident that we will pass a bill to protect the financial security of every American very soon."

A key House negotiator, Rep. Barney Frank, has also said he believes a deal can be in place by Sunday.

The bailout is intended to rescue bankers from the bad loans that threaten to derail the economy and plunge the country into a long depression. With talks set to resume, negotiators sought a deal before Asian markets open Monday.

House Republicans are now negotiating to give the Treasury the option to make loans to financial institutions in lieu of buying distressed assets.

A House Republican said this would be "better for taxpayers."

Pelosi told fellow Democrats during a private meeting Friday that the legislation would not let judges rewrite mortgages to help bankrupt homeowners avoid foreclosure. That provision amounted to a deal-breaker for Republicans, whose votes are needed to pass the measure, she said, according to lawmakers at the meeting.

Democrats and Bush administration officials said they were willing to include House Republicans' idea of having the government insure distressed mortgages β€” but only as an option, rather than a replacement for the administration's more sweeping approach.

In a sign of movement, House Republicans also dispatched their second-ranking leader, Rep. Roy Blunt of Missouri, to join the talks after their objections to an emerging compromise had brought negotiations to a standstill.

Negotiators broke past midnight without an agreement. The House was in session Saturday, but action on the bailout plan is expected to be focused on the Senate side, where the bipartisan, bicameral negotiations are taking place.

"I'm convinced that by Sunday we will have an agreement that people can understand on this bill," said Frank, a key Democrat in eight days of up-and-down talks designed to stave off an economic disaster.

Pelosi added that "progress is being made," although neither she nor Frank divulged details at a late-afternoon news conference in the Capitol.

Democratic and Republican staff aides met into the night on Capitol Hill, going line by line through legislative proposals in an attempt to clear the way for lawmakers to bargain over the weekend.

The major party presidential contenders β€” Republican John McCain and Democrat Barack Obama β€” agreed during their debate Friday that Congress must act soon.

Meanwhile, new details emerged of a remarkably tumultuous White House meeting on Thursday. With the session breaking up in disarray, according to two participants, President Bush issued an appeal, saying, "Can't we just all go out and say things are OK?" The group around the table, congressional leaders as well as McCain and Obama, spurned the presidential request for a publicly united front.

Earlier in the White House meeting, Democrats peppered House Republican leader John Boehner of Ohio with questions about the details of an alternative he was backing. "I don't know what the hell they are," Bush said at one point," recalled one person who was in the room. All the participants spoke on condition of anonymity, saying the meeting was private.

The legislation the White House is promoting would allow the government to buy bad mortgages and other sour assets held by investors, most of them financial companies. That should make those companies more inclined to lend and lift a major weight off the national economy that is already sputtering.

But a significant number of lawmakers, including many House conservatives, say they're against such heavy federal intervention. Under the GOP plan, the government would insure the distressed securities rather than buy them. Tax breaks would provide additional incentives to invest.

In an Associated Press-Knowledge Networks poll, only 30 percent of those surveyed expressed support for Bush's package. Forty-five percent were opposed, with 25 percent undecided. The survey was conducted Thursday and had a margin of error or plus or minus 3.8 percentage points.

The House was scheduled to convene at 1 p.m. EDT Sunday and members there were hoping they could vote on it by that evening and go home to campaign for re-election. The Senate isn't scheduled to go back into session until Monday morning.

FOX News' Trish Turner and Chad Pergram, FOX Business Network's Peter Barnes, and The Associated Press contributed to this report.