House Republicans are continuing closed-door talks after meeting with President Barack Obama for almost 90 minutes Thursday to discuss a possible short-term extension of the nation's debt limit. Those negotiations - the most serious talks to date on the fiscal impasse - were expected to continue into Thursday evening.

“We had a very useful meeting, it was clarifying for both sides as to where we are,” House Majority Leader Eric Cantor told reporters after the White House meeting. “Our teams are going to be talking further tonight. We'll have more discussion. We will come back to have more discussion. The President said that he would go and consult with the administration folks and hopefully we can see a way forward after that.”

Another Republican, House Appropriations Chairman Hal Rogers, R-Ky., said that negotiators are also trying to "figure out a way to settle the CR [government funding] question" that has pushed a federal shutdown into its second week.

In a statement, the White House called it a "good meeting," although "no specific determination was made" about how to fix the fiscal impasse.

"The President looks forward to making continued progress with members on both sides of the aisle. The President’s goal remains to ensure we pay the bills we’ve incurred, reopen the government and get back to the business of growing the economy, creating jobs and strengthening the middle class."

Republican House Speaker John Boehner speaks to the media on Capitol Hill Thursday ahead of an afternoon meeting at the White House.

In their own statement, GOP leaders said "no final decisions were made; however, it was a useful and productive conversation."

"The President and leaders agreed that communication should continue throughout the night," the joint statement read. "House Republicans remain committed to good faith negotiations with the president, and we are pleased there was an opportunity to sit down and begin a constructive dialogue tonight."

GOP leaders are proposing extending the nation’s debt limit for six weeks to allow for budget negotiations, but the original plan would have done nothing to end the ongoing federal shutdown.

Obama met with 20 top House Republicans for over an hour at the White House Thursday to address the GOP proposal. The government is slated to run out of borrowing power on Oct. 17, the Treasury Department says.

Republicans were tight-lipped about the meeting, avoiding a gaggle of press after the leaving the White House.

Meanwhile, Senate Majority Leader Harry Reid has teed up test votes on a possible debt limit raise by Saturday. The Senate Democrats' current proposal would extend the debt ceiling through the end of 2014, after the midterm elections, but that language could be amended to include any deal that House Republicans negotiate with the president in the interim.

Earlier Thursday, the prospects for compromise looked somewhat bright.

White House press secretary Jay Carney called the GOP proposal "encouraging" and told reporters Obama would likely sign such legislation.

"The president is happy that cooler heads at least seem to be prevailing in the House," Carney said at the daily press briefing. He added: "I think the president said the other day, if they were to send him a clean debt ceiling extension, no partisan strings attached he would sign it. But we don't know that's what we're going to get here."

Stocks were up sharply Thursday morning amid the signs of potential progress on the debt ceiling extension, something Wall Street has been paying close attention to as next week’s expected October 17 debt ceiling deadline looms.

After an earlier closed-door meeting with fellow Republican, Boehner called the proposal "a good-faith effort on our part to move halfway to what [Obama] is demanding in order to have these conversations begin."

Republicans and Democrats are debating a possible short term debt extension, but it's uncertain what each side would have to give. NBC's Mark Murray discusses.

But when asked following a meeting with the president whether Democrats would negotiate with the GOP before the government reopens, Senate Majority Leader Harry Reid, D-Nev., responded curtly: "Not going to happen."

An extension of the debt ceiling, without conditions, would represent somewhat of a concession to Obama, who has demanded that Republicans both reopen the government and raise the government’s debt limit – even for a short period of time – as a precondition to sitting down at the bargaining table.

“Re-open the government, extend the debt ceiling,” Obama said Tuesday afternoon at the White House. “If they can't do it for a long time, do it for a period of time in which in which these negotiations are taking place.”

NBC News’ Luke Russert, Frank Thorp and Kristen Welker contributed reporting.

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