* Lawmakers from both parties say meeting could lead to end of standoff
* Debt ceiling agreement may be close
* Quick end to shutdown also under discussion
* Republicans battered in polls
By Richard Cowan and Tim Reid
WASHINGTON, Oct 10 (Reuters) - President Barack Obama and Republican leaders appeared ready to end a political crisis that has shuttered much of the U.S. government and pushed the country dangerously close to default after meeting at the White House on Thursday.
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 Oct. 17 deadline. One senior Republican said an agreement could come on Friday, though hurdles remain.
The plummeting standing of congressional Republicans in public opinion polls helped spur a move toward ending the standoff, Oklahoma Republican Representative James Lankford said on CNN Thursday night. The latest, an NBC-Wall Street Journal survey published on Thursday, showed the public blaming Republicans by a 22-point margin - 53 to 31 percent.
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 Oct. 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 Oct. 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.
Many hurdles remain. Obama has said he will not negotiate on anything until Republicans agree to reopen the government and remove the threat of immediate default.
Rank-and-file Republican conservatives who remain focused on defeating "Obamacare" also could reject the deal. Even if disaster is averted for now, the entire dispute could come to the fore again when the temporary agreement expires.
House Speaker John Boehner's grip over his troops has been tenuous this year and many of the chamber's most conservative lawmakers have defied him repeatedly on other crucial votes.
Boehner has taken pains to show his party's most rebellious members that he listens to their concerns. He took a different approach when he told them of his plan to extend the debt ceiling.
"He put his best Coach Boehner voice and demeanor on and said, 'Guys, this is what we are going to do. The play has been called. I'm happy to answer questions,'" said Republican Representative Tom Cole of Oklahoma.
The Obama administration says it will be unable to pay all of its bills if Congress does not raise the $16.7 trillion debt ceiling by Oct. 17. Treasury Secretary Jack Lew said he would be unable to prioritize some payments over others among the 30 million transactions his department handles each week.
"It would be chaos," Lew told the Senate Finance Committee.
But Lew and Federal Reserve Chairman Ben Bernanke told their counterparts of the G20 group of economies on Thursday that the standoff over the debt ceiling will be resolved by Oct. 17, Russian Finance Minister Anton Siluanov said.
"Colleagues from the U.S. Treasury and the Federal Reserve have said that they hope to solve the issue soon. They said that the problem will be solved by the 17th," Siluanov told reporters after a dinner with G20 counterparts gathering on the sidelines of the IMF/World Bank meetings.
"It's an important issue for everyone. Both Lew and Bernanke believe that these difficulties can be overcome soon," Siluanov added.
Democrats who control the Senate are readying a vote, possibly on Saturday, that would extend government borrowing authority for more than a year, rather than the weeks-long time frame Republicans have proposed. Still, they did not entirely dismiss the Republican plan.
"Let's see what they have offered," House Democratic Leader Nancy Pelosi said.
House leaders canceled a recess planned for next week and said they would remain in Washington instead.
Opinion polls indicate that Republicans appear to be getting more of the blame for the standoff. The NBC/Wall Street Journal poll released on Thursday found approval of the Republican Party at 24 percent, a record low. Democrats won the approval of 39 percent of the U.S. public.
Business groups that have close ties to the Republican Party have pressed for an end to the brinkmanship and some are laying plans to mount primary challenges next year to lawmakers who refuse to raise the debt ceiling.
Hundreds of thousands of federal employees have been thrown out of work by the shutdown and individual businesses, from arms makers to motels, have begun to lay off workers as well.
The Labor Department said on Thursday that 15,000 private-sector workers have filed for unemployment benefits due to the shutdown.