Mr. Geithner appealed to lawmakers to raise the debt ceiling “this time without the drama and the pain and damage that it caused the country last July.” And he said an orderly solution could be reached.

“Our objective should be to replace that very large set of expiring tax provisions and broad-based, automatic, pretty crude spending cuts with a more responsible, balanced glide path to fiscal sustainability,” he said.

Next year’s fiscal crisis has been brewing since early last decade, when successive Republican Congresses used budget rules to pass large but temporary tax cuts that could not be filibustered. The tax cuts expire en masse at the end of this year after Mr. Obama and Republican leaders agreed on a two-year extension. But the president has vowed not to extend the tax cuts for upper-income families again. Regardless of the election results, he will still be in the White House on Jan. 1.

Senator John Kerry, Democrat of Massachusetts, said: “The American people are tired of kicking things down the road. We’ve got to get this done and done the right way.”

Top aides to Mr. Romney declined to say whether the campaign planned his speech to coincide with Mr. Boehner’s. But as Mr. Romney’s presidential campaign merges its operations more fully with the Republican establishment in Washington, the messages are becoming more similar. Republicans also have indicated they were eager to shift the discussion from social topics like same-sex marriage back to economic issues, which they believe play more to their advantage.

“The Obama campaign wants everybody to be distracted by shiny objects,” said Rich Beeson, Mr. Romney’s political director. “He promised he would cut the debt, and he has not done that.”

The exchange on fiscal policy came on the eve of a Senate budget showdown engineered by Republicans using an obscure procedural provision that says any senator can bring forward a budget if the Budget Committee fails to produce one by April 1.