Reid said that while other Republican leaders were willing to negotiate in good faith, Cantor "has shown he shouldn't even be at the table."
The United States hit its current $14.3 trillion debt ceiling in May and the Obama administration says the government will default on its obligations if the debt limit is not increased by Aug. 2. For a new debt ceiling to last to the end of 2012 would require raising it by about $2.4 trillion.
Republicans, in control of the House of Representatives in part because of the support of tea party activists, say they will not vote to raise the limit if Obama doesn't agree to at least an equal amount of deficit reductions over 10 years.
Obama and the top eight House and Senate leaders met for the fourth time in as many days Wednesday, and, despite the tense ending, agreed to meet again Thursday.
A congressional aide said the White House discussed with lawmakers the possibility of moving talks this weekend to the presidential retreat at Camp David in Maryland. But a spokesman for House Speaker John Boehner said the Ohio Republican told the White House he saw no need for that. And Obama aides later said they planned to continue holding meetings at the White House for the next few days.
Despite McConnell's assertions that the debt problem belongs to Obama, fresh polling from Quinnipiac University suggested voters would be more apt to hold Republicans responsible than Obama, by 48 percent to 34 percent, if the debt limit is not raised. The same survey showed voters were about evenly split on whether they're more concerned about raising the limit and increasing government debt, or seeing the government go into default and damaging the economy.
"The American people aren't very happy about their leaders, but President Barack Obama is viewed as the best of the worst, especially when it comes to the economy," said Peter Brown, assistant director of Quinnipiac's Polling Institute.
That helps explain why McConnell put forward a plan that would give Obama new powers to overcome Republican opposition to raising the debt ceiling.
The proposal would place the burden on Obama to win debt ceiling increases up to three times, provided he was able to override congressional vetoes — a threshold Obama could manage to overcome even without a single Republican vote and without massive spending cuts. Conservatives promptly criticized the plan for giving up the leverage to reduce deficits. But the plan raised the prospect of combining it with some of the spending cuts already identified by the White House in order to win support from conservatives in the House.
In an interview with radio talk-show host Laura Ingraham, McConnell described his plan in stark political terms, warning fellow conservatives that failure to raise the debt limit would probably ensure Obama's re-election in 2012. He predicted that a default would allow Obama to argue that Republicans were making the economy worse.
"You know, it's an argument he has a good chance of winning, and all of a sudden we (Republicans) have co-ownership of a bad economy," McConnell said. "That's a very bad positioning going into an election."
Sen. Charles Schumer, D-N.Y., said that while the president and other Democrats would still prefer a larger agreement, McConnell's plan was an acceptable option — especially if some consensus spending cuts were added. He said McConnell and Reid were discussing the idea.
Democratic officials said that even as Obama confronted Cantor and Boehner in Wednesday's meeting, he commended McConnell.
"Sen. McConnell at least has put forth a proposal," a Democratic official quoted the president as saying. "It doesn't reduce the deficit and that's what we have to do. It just deals with the debt limit. Now Sen. McConnell wants me to wear the jacket for that."
The officials said Obama went on to say they all had a responsibility to find a compromise.
Associated Press writers Dave Espo, Laurie Kellman, Ben Feller, Julie Pace, Martin Crutsinger and Erica Werner in Washington and Pallavi Gogoi in New York contributed to this report.
- Live at the GOP convention: Donald Trump...
- No sign of Trump endorsement, but plenty of...
- Trump speechwriter apologizes for Melania...
- Thunderous boos for Cruz for refusing to...
- 17 arrested in flag-burning melee outside GOP...
- Trump's moment: Speech to close GOP...
- Cruz: Not supporting candidate who wages...
- Rupert Murdoch vows Fox News without Ailes is...
- Utah delegates finally stand and cheer... 93
- Utah GOP delegates finally fired up... 74
- Obama rejects Trump depiction of US in... 40
- The day after: Lee defends Cruz at GOP... 32
- Trump speechwriter apologizes for... 27
- Police give all-clear in Munich... 27
- Thunderous boos for Cruz for refusing... 22
- Ohio Mormon offered invocation at... 22