WASHINGTON (AP) -- 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 insurance program demanded by House Republicans as an alternative to devoting the entire $700 billion 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.

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

Presidential politics again played a role in the bargaining. Republican John McCain and Democrat Barack Obama called key negotiators and portrayed themselves as helping without getting directly involved in the talks.

Bush expressed confidence earlier Saturday that lawmakers soon would approve a rescue plan while acknowledging that many Americans are frustrated and angry at the amount of money taxpayers are being asked to put up for covering Wall Street firms' mistakes.

The president spoke with Paulson, McCain and other Republican lawmakers during the day, said White House spokesman Tony Fratto.

Under the plan being considered, the Treasury Department would buy deeply distressed mortgage-backed securities. The money should help troubled lenders make new loans. The government would later try to sell the discounted loan packages at the best possible price.

House Republicans were insisting that some of the money be available to insure, rather than buy, distressed mortgage-backed securities. Banks and investment firms holding such packages would pay the government for insurance against losses if the mortgages default.

Proponents say their idea would require less taxpayer spending. But the Treasury Department has said it would not pump enough money into the financial sector to make credit sufficiently available.

Another proposal would have the government receive stock warrants in return for the bailout relief, ensuring that proceeds from eventual sales of the discounted packages would return to the Treasury.

Negotiators were trying to settle on a means of limiting severance packages for executives of companies that benefit from the rescue plan.

They also discussed phasing in the program's costs. For example, after the first $350 billion or so is made available, Congress could try to block later amounts if it believed the program was not working. The president presumably could veto such a move, however, requiring extra large margins in the House and Senate to override.

House Republicans insisted on several changes to the administration's original proposal.

"We should not be bailing out Wall Street on the backs of American taxpayers," House Minority Leader John Boehner, R-Ohio, told reporters at midafternoon, when Paulson and key House and Senate members took over the negotiations from their aides.

Senate Majority leader Harry Reid, D-Nev., said earlier that the goal was to come up with a final agreement before the Asian markets open Sunday night. "Everybody is waiting for this thing to tip a little bit too far," he said, so "we may not have another day." Whatever emerges "is not the proposal that we got from Secretary Paulson," Reid said. But lawmakers said it would be much closer to Paulson's original plan than to the alternative offered by House Republicans several days ago.

McCain, who flew to Washington after Friday night's presidential debate in Mississippi, spent part of Saturday working the phones and "helping out as he can," aide Mark Salter said. But McCain did not enter the Capitol, where his colleagues were voting on a $634 billion spending bill that ended a ban on drilling off the Atlantic and Pacific coasts, and sent billions of dollars to the military.

McCain supports such measures. But the vote would have been difficult for him because the bill also included more than 2,000 pet spending projects worth more than $6 billion. That is the kind of pork-barrel spending that McCain has pledged to end.

Obama campaigned in North Carolina and Virginia. Aides said he placed calls to Paulson, Reid and a key House member to keep tabs on the finance negotiations.

Both presidential candidates are trying to position themselves to take at least partial credit if an accord is reached. Obama spokesman Tommy Vietor offered new details from Thursday's contentious White House meeting that underscored the divisions among lawmakers trying to reach an agreement.

He said Obama encouraged Paulson to work with House Republicans. Since then, Vietor said, Obama has urged negotiators to find a compromise with enough options so the treasury secretary has the flexibility "to act in an effective manner to stem this crisis."