Citing a Democrat familiar with the talks, The Hill reported negotiators will likely meet during the weekend. A short time after Thursday's talks ended without an agreement, the White House said President Barack Obama will hold a news conference at 11 a.m. EDT Friday.
The source told The Hill Thursday's talks were "cordial," in contrast to Wednesday's session, when Obama said he's willing to put his presidency on the line to get a long-term agreement on the budget and the debt ceiling.
A Republican aide said Thursday's session was "composed and polite" and one Hill source said House Majority Leader Eric Cantor, R-Va., remained silent during the meeting.
Obama told negotiators Thursday it's "decision time," the Democratic source told The Hill.
Treasury Secretary Timothy Geithner told negotiators global financial markets want an increase in the federal debt limit as well as "a plan to deal with our deficit and debt," the Republican source told the newspaper.
The credit rating firm Standard and Poor's said Thursday there is a 50-50 chance it will downgrade the U.S. credit rating within three months.
In a statement, the agency said it has placed the federal government on "CreditWatch with negative implications" status. The agency said Thursday's development was indication of its "view that, owing to the dynamics of the political debate on the debt ceiling, there is at least a one-in-two likelihood that we could lower the long-term rating on the U.S. within the next 90 days."
"The political debate about the U.S.' fiscal stance and the related issue of the U.S. government debt ceiling has, in our view, only become more entangled," the statement said.
The move is the latest in a series of steps rating houses are taking to apply pressure on the United States to raise the debt ceiling, saying failure to raise the limit could result in a lower credit rating.
A GOP source speaking on condition of anonymity told CBS News Obama told Republican negotiators Wednesday he has reached his "limit."
"This may bring my presidency down, but I will not yield on this," Obama said after negotiations broke down Wednesday, the source told CBS.
In an interview Thursday with KYW-TV, Philadelphia, Obama said his relationship with Cantor was "cordial."
"At a certain point, the American people run out of patience if they think that people are playing games and not serious in terms of solving problems," he said.
Cantor told reporters Wednesday Obama became so irritated as to assert no president should have to put up with such uncompromising lawmakers.
"That's when he got very agitated and said I've sat here long enough -- that no other president -- Ronald Reagan -- would sit here like this -- and that he's reached the point that something's gotta give," CNN quoted Cantor as saying.
U.S. Sen. Claire McCaskill, D-Mo., speaking on MSNBC Thursday, said the government could save $1 trillion or more by closing corporate tax loopholes.
"Easily $1 trillion over the next 10 years -- and probably multiple to that, depending on whether you go all the way for the mortgage deduction or you go all the way towards charity deductions," McCaskill said. "And I think there's ways that we can craft this that we can maintain those deductions for the middle class, but level the playing field for everybody else."
Meanwhile, rank-and-file GOP House members Thursday held a news conference to urge Obama to maintain Social Security and Medicare commitments, with or without a long-term deal.
"We ask that you make an immediate, clear and unequivocal public commitment that your administration will continue to make all interest payments on time, as well as ensuring the pay of our military personnel, and making Social Security and Medicare payments in full," a letter signed by 57 House Republicans said.
While negotiations at the White House faltered, it appears the Senate Gang of Six may be back on track to talk budgets and deficits, The Hill reported. The five active members of the gang met for more than two hours Wednesday night to renew their push for a deal, and Sen. Tom Coburn, R-Okla., who left the group in frustration in May, said he is thinking about coming back to the fold, The Hill said.
Letting the U.S. government default on its debts would cripple Republicans in the next elections, Senate Minority Leader Mitch McConnell, R-Ky., warned.
"All of a sudden we have co-ownership of a bad economy. That is very bad positioning going into an election," McConnell said on "The Laura Ingraham Show," a conservative radio talk program.
President Obama would be able to "say Republicans are making the economy worse," McConnell said. "It is an argument that he could have a good chance of winning."
McConnell pushed a plan he proposed Tuesday that would let a debt-limit increase clear Congress without Republican approval by giving Obama authority to raise the debt ceiling on his own -- and Congress would vote to disapprove a request instead of approve one.
This would also let Obama raise the debt ceiling without having to guarantee spending cuts.
Sen. John McCain, R-Ariz., said: "I strongly support Sen. McConnell's efforts to avoid a default on our nation's debt, and the last-case emergency proposal he outlined ... to ensure that Republicans aren't unduly blamed for failure to raise the debt ceiling."
But Cantor rejected McConnell's proposal, vowing to press for rolled-back government spending.
McCaskill, speaking on MSNBC's "Morning Joe," said she thinks McConnell has "lost his mind."