WASHINGTON — President Obama intensified his pressure on House Republicans on Tuesday, calling on them to “lift these threats from our families and our businesses” as the federal government remained shuttered into a second week and the possibility that the United States would default on its debts grew closer.

Mr. Obama, holding firm to the position he first took more than a year ago, said at a lengthy news conference that he would not negotiate over the essential act of raising the nation’s debt limit or offer concessions to the Republican-led House to finance and reopen the government.

But he raised the possibility of reopening the government and raising the debt limit in the short term to allow negotiations, a development Republicans saw as positive. “If they can’t do it for a long time, do it for the period of time in which these negotiations are taking place,” he said.

Congress has a constitutional responsibility to both finance the government and keep it solvent, Mr. Obama said, and once the House acts, he will talk.