To get the government up and running again, "it will take some coming together on the Republican side," said the House's lead Democrat, Rep. Nancy Pelosi of California.
"It's very hard to negotiate with the Republicans when they can't negotiate with themselves," Pelosi told MSNBC on Friday.
Obama criticized House Speaker John Boehner, R-Ohio, for not bringing up a vote to finance the full reopening of the government without conditions.
"Speaker John Boehner won't even let the bill get a yes-or-no vote, because he doesn't want to anger the extremists in his party. That's all. That's what this whole thing is about," Obama said Thursday at a campaign-style event at a Rockville, Md., construction company.
Boehner and other Republicans put the blame on Obama. They say he should recognize the flaws of "Obamacare" and negotiate solutions as part of a deal to end the shutdown that forced the furlough of some 800,000 workers, more than a third of federal civilian employees.
Bohener said Obama was being "irresponsible."
On Friday, the Republican-led House was keeping up a drive to finance certain agencies and programs on a piecemeal basis — a strategy rejected by Obama and the Democratic-led Senate.
"We are not picking winners and losers," Rep. Marsha Blackburn, R-Tenn., said Friday on MSNBC. "I think what we are doing is exercising stewardship over the taxpayers' dollars. ...I'm ready to go to work today and get it done."
The House planned a vote to fund a popular program providing food aid to pregnant women and their children, as well as ongoing disaster relief.
Furloughed federal workers were expected to get some relief with legislation authorizing back pay due for a vote on Friday or Saturday in the House. Some top Democrats have supported that idea alongside Republicans.
Obama had been scheduled to leave Saturday for economic summits next week in Indonesia and Brunei. His decision to cancel those plans underscored how entrenched both sides were in a partisan showdown with no end in sight.
Secretary of State John Kerry flew to Bali, Indonesia, on Friday to head the U.S. delegation to the summits.
"The cancellation of this trip is another consequence of the House Republicans forcing a shutdown of the government," White House press secretary Jay Carney said in a statement. "This completely avoidable shutdown is setting back our ability to create jobs through promotion of U.S. exports and advance U.S. leadership and interests in the largest emerging region in the world."
Lawmakers said the shutdown that began Tuesday when the government began its new budget year seemed to be quickly merging with a more critical showdown over the nation's expiring line of credit, raising the stakes for the still-fragile economy.
Obama and his Treasury Department said failure to raise the nation's borrowing limit, expected to hit its $16.7 trillion cap in mid-October, could precipitate an economic nosedive worse than the recent Great Recession. A default could cause the nation's credit markets to freeze, the value of the dollar to plummet and U.S. interest rates to skyrocket, according to a Treasury report.