The fate of a rescue package for the nation’s faltering financial system tottered Thursday as House Republicans balked at a House-Senate deal and a White House meeting ended without resolution.

Disgruntled House Republicans refused to sign on to a bipartisan $700 billion rescue plan announced earlier Thursday and offered up a different proposal.

And although many lawmakers had hoped a deal would be announced Thursday after the White House meeting featuring presidential candidates Sens. Barack Obama (D-Ill.) and John McCain (R-Ariz.) and Congressional leaders, the meeting broke up with the participants going before waiting television cameras with no agreement on what to do, but to say only that something must be done and done quickly.

Senate Majority Leader Harry Reid (D-Nev.) said he and Minority Leader Mitch McConnell (R-Ky.) were still prepared to proceed with the outlines of a deal. “We’re going to begin again tonight at 8 o’clock to see if we can put this train back on the tracks,” Reid said.

House Republicans rejected the idea of buying up troubled bank assets — the core of Treasury Secretary Henry Paulson’s $700 billion bailout proposal — and instead proposed creating a mortgage insurance system guaranteeing the value of illiquid, mortgage-backed securities. That insurance proposal would be paid for not by taxpayers, but by charging the banks holding the securities a premium.

It wasn’t immediately clear whether the proposal would have any influence on the negotiations — or whether it would merely give House Republicans who are opposing the bailout an alternative to vote for.

The proposal, announced by House Chief Deputy Minority Whip Eric Cantor (R-Va.) and Budget ranking member Paul Ryan (R-Wis.), emerged from a working group formed by Minority Leader John Boehner (R-Ohio). Boehner pointedly refused to sign on to a bipartisan “agreement on principles” announced earlier in the day.

“As I told our Conference this morning, there is no bipartisan deal at this time,” Boehner said. “There may be a deal among some Democrats, but House Republicans are not a part of it.”

The earlier announcement of a bipartisan agreement at a news conference attended by House and Senate Republicans and Democrats, including Financial Services ranking member Spencer Bachus (R-Ala.), had raised hopes that a deal could be reached relatively quickly.

Bachus’ role proved frustrating to both sides of the aisle. House Financial Services Chairman Barney Frank (D-Mass.) complained that Bachus after the meeting raised additional concerns about the proposal from House Republicans that he hadn’t raised during the meeting.

And some House Republicans privately questioned why he went to a news conference where Frank and others pronounced they had a broad agreement on principles even as Boehner was saying there was no deal.

Bachus put out a statement, saying he wasn’t representing House Republicans: “As I made clear in the meeting this morning, I was not authorized by my colleagues to make any agreement on behalf of House Republicans. There was progress on many issues, but no agreement other than to continue discussions.”

A Democratic leadership aide said Speaker Nancy Pelosi (D-Calif.) told Paulson that he needs to win over GOP Members.

Paulson said he would “try to talk to House Republicans and try to get them on board,” the aide said. Paulson said he would convey to them that “everyone else is on board” and that there are “some ramifications for your split.”

House Democrats could push through a bailout package without Republicans since it has enough support in the Senate and the White House to become law. But Pelosi “doesn’t want to do that. She wants a strong bipartisan vote,” the aide said.

Senate Budget ranking member Judd Gregg (R-N.H.) said he didn’t know whether the process would break down as a result of House Republicans.

“I certainly hope that rational minds will take control of the process on both sides,” Gregg said. “The problem isn’t hypothetical. It’s real.”

But he said he did not think it would be wise to try to pass a Wall Street rescue plan without significant support from House Republicans.

“It would be inappropriate to do this if we don’t have strong bipartisan support across the Capitol,” he said, noting that the markets might not have confidence in the plan if it is not passed by broad majorities in each chamber.

Senate Majority Whip Dick Durbin (D-Ill.) said the mortgage insurance proposal could cause more problems.

“It isn’t going to help,” he said.

The “agreement on principles” passed out to reporters called for allowing the $700 billion to be spent in three tranches, with $250 billion available immediately, and creating a powerful oversight board with the authority to end the program. Congress would also have the option to rescind $350 billion at a later date.

The principles also included a proposal to force companies that avail themselves of the bailout to provide the government with an equity stake in the business, and it would require limits on compensation for executives. The group also would establish three levels of oversight with a new inspector general, Treasury regulations and audits by the Government Accountability Office. Other principles stated the bill should “maximize and coordinate efforts to modify mortgages for homeowners at risk of foreclosure,” but it was unclear how that goal would be achieved.

If the program proved profitable, most of the profits would go to debt reduction, but a percentage would go to affordable housing programs.

“We’re prepared to act expeditiously,” Senate Banking, Housing and Urban Affairs Chairman Chris Dodd (D-Conn.) said.

Sen. Bob Bennett (R-Utah) said he was encouraged by the bipartisan nature of the talks. “We will indeed have a plan that can pass the House, pass the Senate, be signed by the president and bring a sense of certainty” to the financial markets, he said.

Sen. Richard Shelby (R-Ala.), ranking member on the Banking Committee, was absent from the meeting. Shelby has come out against the bailout, forcing Bennett to serve as the senior GOP member in the meeting.

Shelby further inflamed the divisions by stepping out of the White House meeting to declare that there is no agreement. Quoting what he said were leading economists, Shelby said, “The Paulson plan is a bad plan. It will not solve the problem. It will create more problems. We are rushing to judgment.”

Still, lawmakers attempted to be upbeat about the prospects for passage of a rescue plan by Sunday.

“At the end of the day, I think something very similar to what we’ve put forth today will occur,” Sen. Bob Corker (R-Tenn.) said. “Hopefully, by Sunday.”

Tory Newmyer and Jennifer Bendery contributed to this report.