US President Barack Obama and Republicans in the House of Representatives failed to agree on a six-week extension of the nation's borrowing authority during a meeting at the White House on Thursday, but the two sides kept talking, and the offer from politically besieged Republicans was seen as a step toward ending the budget stand-off.
In statements that struck the most positive tone in weeks of acrimony, House Republicans described their meeting with Mr Obama as ''a useful and productive conversation'', while the White House described ''a good meeting'', although ''no specific determination was made'' about the Republicans' offer. Both agreed to continue talks through the night.
People familiar with the meeting said Mr Obama pressed Republicans to reopen the government, and that Republicans raised the possibility that financing could be restored by early next week if terms for broad budget negotiations could be reached.
Twenty Republicans, led by House Speaker John Boehner, went to the White House at Mr Obama's invitation after finetuning their offer to increase the Treasury Department's authority to borrow money to pay existing obligations through to November 22. In exchange, they sought the President's commitment to negotiate a deal for long-term deficit reduction and a tax overhaul.
''The President didn't say yes, didn't say no,'' Republican congressman Paul Ryan, chairman of the House Budget Committee, said. ''We're continuing to negotiate this evening.''
The move was seen as an opening gambit in the legislative dance toward some resolution before the government is expected to breach its debt limit on Thursday. Even before the meeting, the White House and its Democratic allies in Congress were all but declaring victory at the evidence that Republicans - suffering the most in opinion polls, and pressured by business allies and donors not to provoke a default - were seeking a way out of the impasse.
The governors of at least four states expressed interest in an offer from Interior Secretary Sally Jewell to allow them to reopen national parks, although it remained unclear whether any such deals could be reached soon.
Ms Jewell said the Obama administration would be willing to consider such agreements as long as the states agreed to pay the full operating costs, including the salaries of all federal park employees.
''South Dakota, Utah, Colorado and Arizona have all expressed some initial interest in exploring a potential agreement,'' Blake Androff, chief spokesman for the Interior Department in Washington, said.
Arizona Governor Jan Brewer had offered to pay to partly reopen Grand Canyon National Park, at a cost of $US30,000 ($31,600) a day, said Andrew Wilder, the Governor's spokesman. But to fully reopen the park would cost far more, he said.
''I think the administration would need to explain why full funding is necessary and why a partial reopen is not possible,'' Mr Wilder said. ''Frankly, it raises suspicions about whether or not they are earnest in their offer.''
Other states said they were uninterested in Ms Jewell's offer.
''[California] has no plans to front the money to reopen the national parks in California,'' said H.D. Palmer, deputy director for external affairs at the California Department of Finance.
He cited uncertainty over the debt ceiling negotiations in Washington as a factor, as well as uncertainty about whether the states would be reimbursed.
''It's unfortunate because a number of communities around national parks, which depend on people visiting the parks, are already feeling the impacts of the shutdown,'' Mr Palmer said.
Burnt by his experience with House Republicans in mid-2011, when brinkmanship over the debt limit hobbled the already weak economy, Mr Obama began his second term vowing never again to negotiate over raising the ceiling.
''The good news is that Republicans have accepted the principle that they're not going to attach conditions to the debt ceiling,'' said Chris Van Hollen of Maryland, the senior Democrat on the House Budget Committee. ''The bad news is they've only extended the debt ceiling for six weeks, which will continue to generate huge amounts of destructive uncertainty in the economy. And, of course, they also continue to keep the government shut down.''
Mr Boehner and his colleagues left the White House without speaking to reporters, and met in his Capitol suite for further discussion.
Before the White House meeting, the administration and congressional Democrats said they were sceptical 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 they say they do not believe the warnings that failing to act could provoke a default and economic chaos globally.
''We'll see what they're able to pass,'' Mr Obama's press secretary, Jay Carney, said.
Mr Ryan said before the White House meeting that Republicans were now willing to 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, such as raising additional tax revenues, that would enrage the party's conservative base heading into the 2014 mid-term congressional elections.
New York Times