Before the White House meeting, administration and Congressional Democrats said they were skeptical that House Republican leaders could pass the proposal. A large faction of Tea Party conservatives campaigned on promises never to vote to increase the nation's debt limit. And Congressional Democrats vowed to oppose any proposal that did not also fully finance a government now shuttered since the fiscal year began Oct. 1.
"We'll see what they're able to pass," said Mr. Obama's press secretary, Jay Carney.
Senate Democrats had their own White House meeting with Mr. Obama and Vice PresidentJoseph R. Biden Jr. three hours before the House Republicans arrived, and the majority leader, Senator Harry Reid of Nevada, declined to embrace the Republicans' debt limit proposal until he saw it. He told reporters that Democrats would not negotiate on further deficit reductions until House Republicans agreed to the measure passed by the Senate to finance and open the government through mid-November.
"Not going to happen," Mr. Reid said. "Open the government," he added. "There is so much pain and suffering out there. It is really tear-jerking, to say the least."
Separately, members of the Senate's Republican minority, who are to meet with Mr. Obama on Friday, worked on a proposal for full-year government funding — at levels reflecting the across-the-board spending cuts known as sequestration, but giving agencies flexibility to shift money around. They are considering adding it to any short-term debt limit increase that the House might pass and send to the Senate.
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Mr. Ryan said before the White House meeting that Republicans were now willing to formally negotiate with Senate Democrats over a long-term, comprehensive budget framework. The Republicans have resisted such a move since April, fearing that it would require compromises, like raising additional tax revenues, that would enrage the party's conservative base heading into the 2014 midterm elections.
Many House Republicans, leaving a closed-door party caucus earlier Thursday that at times grew contentious, said they would support their leadership's short-term debt limit proposal. But they said they would do so only if Mr. Obama agreed to negotiate a broader deficit reduction deal, with big savings from entitlement programs.
The president has insisted he will not agree to significant reductions in projected Medicare and Medicaid spending — even his own tentative proposals — unless Republicans agree to raise revenues by curbing tax breaks for corporations and wealthy individuals. And Mr. Boehner in recent days reaffirmed the party's anti-tax stance, which suggests that future talks could founder.
Economists across a broad spectrum agree that breaching the debt limit would damage the economy. The new Republican proposal could temporarily remove that threat.
—By Jackie Calmes and Ashley Parker of The New York Times. Jeremy W. Peters and Annie Lowrey contributed reporting.