Democrats and Republicans were nearing agreement on the rescue legislation, the most sweeping government intervention in the market since the Great Depression, and set a meeting early Thursday to begin drafting a bipartisan bill.
Bush acknowledged in a prime time television address Wednesday night that the bailout would be a "tough vote" for lawmakers.
"Without immediate action by Congress, America could slip into a financial panic, and a distressing scenario would unfold," Bush said as he worked to resurrect the unpopular bailout package.
The president's dire warning came not long after he invited Obama and McCain, one of whom will inherit the economic mess in four months, as well as key congressional leaders to a White House meeting on Thursday to work on a compromise.
Bush strongly urged Congress to act quickly to pass the plan, warning Americans in his 12-minute speech that failing to act fast risked dire economic consequences such as disappearing retirement savings, rising foreclosures, lost jobs and closed businesses.
With the administration's original proposal considered dead in Congress - even McCain called it flawed - top House leaders issued an upbeat statement late Wednesday saying there was progress toward revised legislation that could pass.
"We are committed to continuing to work cooperatively and on a bipartisan basis to safeguard the interests of the American taxpayers," said Speaker Nancy Pelosi, D-Calif., and House Republican leader John Boehner of Ohio.
Sen. Dick Durbin of Illinois, the Senate's No. 2 Democrat, expressed optimism that Congress could work through the weekend and pass the measure, possibly by the time markets open on Monday.
Rep. Barney Frank, D-Mass., a lead negotiator on the package, said given the progress of the talks, the White House meeting scheduled for Thursday afternoon was a distraction.
"We're going to have to interrupt a negotiating session tomorrow between the Democrats and Republicans on a bill where I think we are getting pretty close, and troop down to the White House for their photo op," said Frank, the House Financial Services Committee chairman. "I wish they'd checked with us."
The heart of the unprecedented plan, unveiled less than a week ago, involves the government buying up sour assets of shaky financial firms in a bid to keep them from going under and to stave off a potentially severe recession.
Treasury Secretary Henry Paulson and Federal Reserve Chairman Ben Bernanke spent most of the day at the Capitol, shuttling between public hearings on the proposal and private meetings with lawmakers.
Presidential politics intruded, as well, when McCain said he intended to return to Washington and was asking Obama to agree to delay their first debate, scheduled for Friday, to deal with the meltdown.
Obama said the debate should go ahead.
The rivals issued a joint statement calling for a bipartisan effort to deal with the crisis.
"The plan that has been submitted to Congress by the Bush administration is flawed, but the effort to protect the American economy must not fail," the two candidates said. "This is a time to rise above politics for the good of the country. We cannot risk an economic catastrophe."
Pelosi and Boehner said they, too, agreed that "key changes" were needed in Bush's plan.
"It must include basic good-government principles, including rigorous and independent oversight, strong executive compensation standards, and protections for taxpayers."
Earlier, Paulson agreed to demands from critics in both parties to limit the pay packages of Wall Street executives whose companies would benefit from the proposed bailout.
Acknowledging the concession in his speech, Bush said the rescue "should make certain that failed executives do not receive a windfall from your tax dollars."
The administration and congressional negotiators also were nearing accord on parceling out the $700 billion so it would not be available all at once, although key details remained to be worked out.
"People understand it's not going to be a straight $700 billion," Frank said.
Paulson also was said to have accepted the idea of allowing the government to take an equity stake in some of the companies aided - rather than just purchasing their bad assets, as Bush originally proposed - but there was no agreement yet on how the plan would work.
Lawmakers in both parties have strenuously objected to the plan over the past two days, Republicans complaining about federal intervention in private business and Democrats pressing to tack on help for beleaguered homeowners. But many appear to be open to legislation, although on different terms than the White House has proposed.
"There's politically a lot of pessimism because the American people are pushing back," said Rep. Spencer Bachus of Alabama, the senior Financial Services Committee Republican. But, he added, "There's a realization that we have to do something, and that we can't leave town until we do."
Polls in the past several days have provided mixed messages about the public's view.
An ABC News-Washington Post poll said Wednesday the public is split about evenly over whether it supports federal "steps" to handle the financial crisis. In a survey released Tuesday by the nonpartisan Pew Research Center, there was nearly 2-1 support for the government "potentially investing" billions to try securing the markets.
Democrats insist Republican lawmakers must stand up for their own president's proposal, but they appear anything but eager to do so.
"It's a tough sell to most of our members," Rep. Tom Davis, R-Va., said after a closed-door meeting with Paulson and Bernanke. "It's a terrible plan, but I haven't heard anything better."
Compounding the administration's challenge, Republicans and Democrats both say Bush has lost credibility, particularly in cases where he argues there will be dire consequences if Congress doesn't act.
"They sold the war, they sold the stimulus package and some other things. It's the 'wolf at the door"' argument, Davis said.
Democrats are pushing to allow bankruptcy judges to rewrite mortgages to ease the burden on consumers who are facing foreclosure as part of the plan. But Obama told reporters the provision "is probably something that we shouldn't try to do in this piece of legislation."
Other Democratic demands, to give Congress greater authority over the bailout and require that the government help homeowners avoid foreclosures, already have been accepted in principle.
Associated Press writers Jennifer Loven, Martin Crutsinger, Jeannine Aversa and Alan Fram contributed to this report.