"I think everyone who is concerned about lifting the debt ceiling is saying bravo for Senator McConnell," said House Democratic leader Nancy Pelosi.
But Carney said the White House would rather do something more substantial, a "grand bargain" to significantly cut spending and raise more revenue.
The financial world was watching with growing jitters.
"No one can tell me with certainty that a U.S. default wouldn't cause catastrophe and wouldn't severely damage the U.S. or global economy," Jamie Dimon, CEO of JPMorgan Chase & Co., told reporters Thursday. "And it would be irresponsible to take that chance."
Already, Moody's Investors Service is reviewing the government's credit rating, saying there is a small but rising risk that it will default on its debt. If Moody's were to lower the rating, the consequences could ripple through the economy, pushing up rates for mortgages, car loans and other debts. A Chinese rating agency, Dagong Global Credit Rating Co., also warned of a possible downgrade.
Reid sketched the potential consequences of default in dire terms, saying Social Security checks, veterans' benefits and paychecks for troops would stop. "Millions of Americans could lose their jobs," he added.
A Reid spokesman later clarified that Social Security benefits "could" stop, as Obama previously had warned, but it wouldn't be a certainty.
Republicans have called such statements scare tactics.
In the cauldron of the White House Cabinet Room, Obama and top lawmakers bargained for nearly two hours late Wednesday. Obama curtly ended the session when Cantor, R-Va., urged him to accept a short, monthslong increase in debt instead of one that would last through next year's presidential election.
"Enough is enough. ... I'll see you all tomorrow," Obama said, rising from the negotiating table and leaving the room, according to several officials familiar with the session.
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.
Despite the heightened tensions that have been on display, the White House said there was no talk of shaking up the negotiation process or changing the participants — including the top eight House and Senate leaders.
"These are the leaders of Congress, and this is the president and vice president," Carney said. "These are the people who have to in the end come to an agreement."
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 the White House said there was no plan to move the meetings.
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.
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