WASHINGTON — The US Senate approved a Democratic plan Wednesday to extend expiring tax breaks for all but the wealthiest Americans, though the measure will not resolve the country’s looming fiscal impasse.

Republicans want the Bush-era tax cuts extended for all, arguing that Congress should not raise taxes on anyone when the economy is as sluggish as it is now, but their measure to do just that failed and the chamber passed the Democratic bill instead.

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By a narrow 51-48 vote, lawmakers voted to extend the tax cuts for all American families making less than $250,000 per year. The bill would mean those making more than that figure would pay higher taxes in 2013.

The vote was a Washington political showdown of the first order, with Vice President Joe Biden appearing in the Senate in the event he was needed to break a tie, after two in the Democratic caucus — Joe Lieberman and Jim Webb — said they would vote no on the measure and two others were undecided.

The bill “respects the will of the American people,” Majority Leader Harry Reid said on the Senate floor shortly before the vote.

“We can spend the next five months debating” whether the wealthiest Americans should also receive a tax break, he added.

The bill, however, is likely to fail in the Republican-controlled House of Representatives, ensuring that the debate over taxes carries on deeper into campaign season ahead of November’s general elections.

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“We all know this is not about the economy. We know this is about the election,” Senate Minority Leader Mitch McConnell said.

“This proposal guarantees that taxes will go up on roughly a million of our most successful small businesses,” he said, reflecting the Republican argument that the tax hikes would harm some of the country’s top job creators at a time of persistently high unemployment.