They went around and around for an hour, getting nowhere.
Then came a sudden change that could help break the political impasse causing a partial government shutdown and the looming threat of a further crisis when the nation bumps up against its self-imposed borrowing limit.
As first reported by CNN's Dana Bash and Deirdre Walsh, an exchange between GOP Rep. Paul Ryan and President Barack Obama seemed to clear the air, with each side acknowledging the validity of the other.
Ryan, the Republican chairman of the House Budget Committee, conceded his side wouldn't get all it wanted while Obama said, tell me what you need to make something happen, Bash and Walsh reported after the Thursday night meeting.
CNN Chief National Correspondent John King told CNN's "New Day" on Friday that Ryan "said something to the effect of, 'Look, we know you don't like our position, we know you probably don't respect our position, but we're the Republican majority.' "
"You're stuck with us for a while, at least through the next election season, so we need to learn to have a conversation with each other," King paraphrased Ryan as saying.
"And at that point, both Democrats and Republicans say, the tone of the meeting changed," King added. "The president said, 'Listen, I'm not going to negotiate with you until you reopen the government, but go to your members, find out what you need to do to get that part done and let's try to make some progress.'"
CNN's reporting on the meeting is based on accounts from multiple sources who attended.
Republican Rep. Steve Southerland of Florida essentially confirmed the CNN account on Thursday night.
"Paul and the President certainly have a pass through the last election and I think there's a great respect between them. And you can't make that up." Southerland said, adding that "the communication between Paul and the President, I think, was an important part of the conversation."
The meeting appeared to begin breaking the partisan logjam that has kept parts of the government shut down for 11 days, leaving hundreds of thousands of federal employees without work and causing countless ripple effects, from lost tourist revenue around national parks to a threat to the Alaskan crab fishing season.
"We're all working together now," Rep. Pete Sessions, a Texas Republican, said after the meeting, while House Majority Leader Eric Cantor called the meeting "very useful."
The Obama administration described the meeting as "good," saying the President listened to Republican proposals and the two sides discussed "potential paths forward."
On Friday, Senate Republicans arrived at the White House for their talks with Obama, who has held separate sessions with the House party caucuses as well as Senate Democrats.
Senators are involved in their own talks to come up with a package that would reopen the government and lower the debt ceiling, while ending a tax on medical devices under Obamacare and setting up broader negotiations on deficit reduction.
In a video message to a conservative political summit Friday, Ryan warned the right-wing gathering that they can't get everything they want with Democrats holding the White House and a majority of the Senate.
"This President won't agree to everything we need to do," said the message from Ryan, according to excerpts provided by one of his aides. "A budget agreement with this President and this Senate won't solve our problems. But I hope it's a start."
Beginnings of a deal?
After initially demanding changes to or the elimination of Obama's signature health care reform plan, Republicans have more recently focused on extending the debt ceiling for up to six weeks while negotiating on spending and other issues during a continued government shutdown.
Democrats have insisted that the debt ceiling be raised and the government reopened before they would be willing to negotiate on other issues.
Obama made clear, during his session with House Republicans, that he won't give concessions to reopen the government, according to a Democratic source familiar with the meeting.
But he has indicated willingness to consider a short-term debt deal, a Democratic lawmaker told CNN.
"If that's what (House Speaker John) Boehner needs to climb out of the tree that he's stuck in, then that's something we should look at," according to the lawmaker, who attended the meeting and spoke on the condition of anonymity.
Rep. Hal Rogers, a Kentucky Republican, said both sides are talking "in good faith" about not just the debt ceiling, but also what it will take to restart the government.
"There was not a timeline set," Rogers said. "But we want to move quickly."
Some congressional Democrats have balked at the outline of the GOP offer, insisting the government must reopen and the debt ceiling must be increased to get broader talks going.
"One way or another both of those have to happen," said veteran Sen. Carl Levin of Michigan.
Another Democrat, Rep. Elijah Cummings of Maryland, said Obama "needs to press for the opening of the government."
"Without a doubt the default would be much more catastrophic, but I've got constituents, a lot of whom work for the federal government who are going through catastrophes every hour," Cummings said.
Anti-Obamacare provisions no longer in GOP plans
One thing any agreement won't include, it appears, is a provision to defund the 2010 Affordable Care Act.
Ryan, who was the Republican party's vice presidential nominee last year, didn't mention Obamacare in a Wall Street Journal op-ed this week, saying instead that politicians from both parties should focus on "modest reforms to entitlement programs and the tax code."
As others have done in recent days, GOP Rep. James Lankford of Oklahoma told CNN on Thursday that cutting the funding for the President's signature health reform is "currently off the table."
However, Lankford said Republicans still seek a one-year delay in the penalties under Obamacare for people who fail to obtain health insurance, as required by the law.
Yet Sen. Ted Cruz of Texas -- one of the most vocal Republicans in the debate -- wasn't so ready to let the health care issue go. Speaking Thursday on CNN's "Crossfire," he said, "Democrats in this town do not want to discuss Obamacare."
On Obama's signature health care reform and what's happening in Washington generally, Cruz said that it's House Republicans who "are listening to the millions of Americans" to do what's best for them.
According to a GOP source, it's not certain whether Boehner can gain support from some or most of his GOP caucus for a plan without anything to do with Obamacare or other concessions. That could mean, if a proposal like the one floated Thursday proceeds, the speaker may need Democratic votes to pass it.
Failure to raise the debt ceiling by next week's deadline would leave the government unable to borrow money to pay its bills for the first time in its history. And absent a breakthrough, the shutdown would continue at a cost estimated at up to $50 billion a month.
All of this is taking a toll on Washington's reputation: A national CNN/ORC International survey released Monday indicated that Americans are blaming all parties in the fight, though Republicans got the worst of it.
CNN's Alan Silverleib, Chelsea J. Carter, Paul Steinhauser, Jim Acosta, Barbara Starr, Ted Barrett, Dan Merica and Brianna Keilar contributed to this report.