Mr. Boehner criticized the president for refusing to negotiate with House Republicans, either to finance and reopen the government or to increase the nation’s debt limit so that it does not default on its debts for the first time. “Really, Mr. President, it’s time to have that conversation before our economy is put further at risk,” he said.

Mr. Obama and Congressional Democrats have dug in, telling Republicans to capitulate because it is a basic responsibility of Congress to keep the government solvent and open for business. To give in, the Democrats argue, would only encourage Republicans to demand concessions every time the government needs financing, which happens annually, or an increase in the debt limit, which has occurred more than 40 times since Ronald Reagan became president.

At FEMA, Mr. Obama countered Republicans’ claims that he was refusing to negotiate.

“There is not a subject that I am not willing to engage in, work on, negotiate and come up with common-sense compromises on,” Mr. Obama said. “What I’ve said is that I cannot do that under the threat that if Republicans don’t get 100 percent of their way, they’re going to either shut down the government or they are going to default on America’s debt so that America, for the first time in history, does not pay its bills.”

“We’re not going to establish that pattern,” he added.

Republicans acknowledge that their decision to link the reopening of the government to the health care law is unpopular. A Washington Post/ABC News poll released Monday found that disapproval of Congressional Republicans had jumped to 70 percent, from 63 percent late last month.

But David Winston, a Republican pollster close to Mr. Boehner, said Mr. Obama’s stance was likely to prove unpopular as well. “Anyone who says he knows how this is going to turn out doesn’t know,” Mr. Winston said. “We are in a very unsettled time.”