WASHINGTON — A senior House Republican on Tuesday urged his party’s leadership to embrace the immediate extension of the Bush-era tax cuts for households earning less than $250,000, then fight out the fate of higher-income tax breaks later.

In a private meeting of the House Republican whip team, the group responsible for vote counting, Representative Tom Cole of Oklahoma broke with the rest of the leadership and said the party should join with President Obama for now, Republican aides said. The meeting was first reported by Politico.

"The first thing I’d do is make sure we don’t raise taxes on 98 percent of the American people," he said in an interview Tuesday night. "We’ll get some credit for that, and it’s the right thing to do."

The break came after senior Democrats hardened their line on conditions for a deal to head off the automatic spending cuts and tax increases set to kick in this January. Democrats said Tuesday that Mr. Obama would not accept any deficit reduction deal that did not include a long-term extension of the debt ceiling, possibly ensuring that Mr. Obama would not have to deal with another debilitating fiscal showdown for the remainder of his presidency.