No deal emerged from the 90-minute meeting, but talks continued into the night in an effort to re-open the government and extend the government's borrowing authority beyond an October 17 deadline. One senior Republican said an agreement could come on Friday, though hurdles remain.
The President's meeting with Republican leaders was the first sign of a thaw in a 10-day standoff that has weighed on financial markets and knocked hundreds of thousands of federal employees out of work.
"It was a very adult conversation," said Republican Representative Hal Rogers, who attended the meeting. "Both sides said they were there in good faith."
Republicans in the meeting offered to extend the government's borrowing authority for several weeks, temporarily putting off a default that otherwise could come as soon as next week. Obama pushed to also reopen government operations that have been closed since October 1.
Significantly, Republicans seemed to be steering clear of the restrictions on Obama's healthcare reforms and spending that prompted the crisis in the first place. Instead, negotiations centered on how far to extend the debt limit and how much funding they would provide the government when it opens, according to Republicans.
The two sides are working on "defining parameters to see if we can make progress," said Republican Representative Pete Sessions, a member of the leadership.
"The President looks forward to making continued progress with members on both sides of the aisle," the White House said in a statement.
The proposal is a significant shift for Republicans, who had hoped to use the threat of a shutdown and a default to undermine Obama's healthcare law.
But they have been hammered in opinion polls and pressured by allies in the business community who worry the brinkmanship is killing jobs and slowing the economy. Republicans worry that the standoff could imperil lawmakers in competitive districts, giving Democrats an increased chance of winning control of the House next year.
Now Republicans hope a short-term debt-limit extension, perhaps until the middle or end of November, will buy time to seek spending cuts, a repeal of a medical-device tax, or other measures they say are needed to keep the national debt at a manageable level.
Conflicting reports of the outcome of the meeting sent immediate ripples through financial markets. U.S. equity index futures tracking the S&P 500 index dropped after a report that Obama had rejected the Republican offer, but rose when details of the meeting trickled out. Major U.S. equity indexes closed 2 percent higher earlier on Thursday on hopes of a deal.
DIDN'T STOP OBAMACARE
The crisis began in late September when Republicans tied continued government funding to measures that would undercut the Affordable Care Act, Obama's signature legislative accomplishment.
The gambit didn't work, as "Obamacare" unveiled its online health-insurance exchanges on October 1 even as much of the rest of the government shut down. Even so, the exchanges have been plagued by serious technical problems unrelated to the shutdown.
In recent days, Republican leaders have emphasized other goals, such as reining in the retirement and health benefit programs that pose a long-term threat to the country's fiscal health.
For the first time in weeks, lawmakers from both parties predicted they would be able to resolve their differences.
"Both sides will be able to claim victory," said Democratic Representative Chaka Fattah of Pennsylvania.