Letting the U.S. government default on its debts would cripple Republicans in the next elections, Senate Minority Leader Mitch McConnell, R-Ky., said.
"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.
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 House Majority Leader Eric Cantor, R-Va., rejected McConnell's proposal, vowing to press for rolled-back government spending.
"Currently, there is not a single debt-limit proposal that can pass the House of Representatives," Cantor said in a statement Wednesday before joining seven other top lawmakers from both parties for a White House meeting with Obama and Vice President Joe Biden.
The lawmakers are to return to the White House for another meeting at 4:15 p.m. EDT Thursday.
During Wednesday's meeting, Cantor and Obama had a testy exchange when Cantor pressed for a short-term debt-limit increase that would require Congress to vote a second time on the unpopular measure before the 2012 election.
Obama "got very agitated, seemingly," Cantor said, quoting the president as saying: "Eric, don't call my bluff. I'm going to the American people with this."
Obama then "shoved back and said, 'I'll see you tomorrow' and walked out," Cantor said.
"I was a little taken aback," Cantor added.
Democrats said Obama didn't depart abruptly but did argue that Republicans had been unwilling to compromise.
"Enough is enough," Obama said several times The Washington Post reported, citing Democratic officials.
The tension came as Federal Reserve Chairman Ben Bernanke warned of a "huge financial calamity" if Republicans and Democrats don't agree on a budget deal that lets the debt ceiling be increased.
Two credit-rating agencies also moved closer to an unprecedented downgrade of the U.S. government debt.
Moody's Investors Service said Wednesday it was reviewing the government's top Aaa bond rating for a possible downgrade, citing the "rising possibility" Washington's $14.3 trillion borrowing limit wouldn't be raised soon enough to prevent the government from running out of money to pay its bills.
Standard & Poor's privately told lawmakers and top business groups it might cut the U.S. credit rating if the government doesn't make any of its expected payments -- including Social Security checks -- even if it makes all its debt payments, The Wall Street Journal reported.
S&P assigned U.S. debt a "negative" outlook in April because of "very large budget deficits and rising government indebtedness" with an unclear path toward resolution.