Senate Republicans derailed legislation Saturday to extend expiring tax cuts at all but the highest income levels in a political showdown that paradoxically clears a path for a compromise with the White House on steps to boost the economy.

"We need to get this resolved and I'm confident we can do it," President Barack Obama said shortly after the near party-line votes. The public must have "the peace of mind that their taxes will not go up" on Jan. 1, he added.

Obama has signaled that he will bow to Republican demands for extending tax cuts at all income levels, and his remarks capped a day that lurched between political conflict and talk of compromise on an issue that played a leading role in last month's elections.

Sen. Chuck Schumer, D-N.Y., eyeing the 2012 campaign, accused Republicans of siding with "millionaires and billionaires" with their rejection of proposals that would let tax cuts passed during George W. Bush's presidency lapse on seven-figure incomes.

Republicans noted that unemployment rose to 9.8 percent last month and said it made no sense to raise taxes on anyone in a weak economy. Sen. Jon Kyl, R-Ariz., jabbed that Democrats were undergoing a "political catharsis" in public after losing control of the House and surrendering several seats in the Senate in the Nov. 2 election.

But the rhetoric subsided quickly after the votes, and Senate leaders in both parties said they hoped political clashes would give way to compromise in the next several days.

Kentucky Sen. Mitch McConnell, the GOP leader, said he was relatively confident there would be a deal with the White House "not to raise taxes in the middle of a recession." He said talks were continuing on the length of an extension to be enacted for the cuts that were put in place in 2001 and 2003.

Senate Majority Leader Harry Reid, D-Nev., said he hoped for an agreement by the middle or end of next week on legislation that would combine an extension of tax cuts with a renewal of expiring jobless benefits for the long-term unemployed.