WASHINGTON — Senate Democrats narrowly approved a plan to preserve tax cuts for the middle class while letting them expire for the wealthy on Wednesday, giving Democrats a significant political victory on a measure that is fated to go no further in Congress.

Senators approved the bill by a near party-line 51-48 vote, with Vice President Joe Biden presiding over the chamber in case his vote was needed to break a tie. Minutes earlier, lawmakers voted 54-45 to kill a rival Republican package that would have included the best-off in the tax reductions.

The $250 billion Democratic measure would extend tax cuts in 2013 for millions of Americans that otherwise would expire in January. But it would deny those reductions to individuals making over $200,000 yearly and couples earning at least $250,000.

Passage of the Democratic measure put the Senate on record as backing a bill that closely follows the tax-cutting vision of President Barack Obama. It averted what would have been a significant embarrassment for Democrats and Obama, who has made tax fairness an overarching theme of his re-election campaign.

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The vote also serves as a counterpoint to the GOP-run House, which next week will approve tax cuts nearly identical to the $405 billion Republican plan the Senate rejected Wednesday.

Sen. Susan Collins, who along with Sen. Olympia Snowe voted with their Republican colleagues against the plan, said she favored a complete overhaul of the tax system instead. She also said the Democratic plan did not do enough to protect small businesses.

“The Democrats’ proposal, which is backed by the administration, would not only raise taxes on hard-working families, but also allow the ‘death’ tax to rise to a confiscatory top rate of 55 percent on estates, with only $1 million exempted,” she said in a statement. “This would make it virtually impossible for far too many small, family-owned businesses and family farms to be passed on to the next generation.”

Snowe also favors comprehensive tax reform.

“I voted to extend tax relief for all Americans because, as the Congressional Budget Office recently reported, a failure to address impending policy decisions such as the sequester and expiration of the current tax rates could have a negative impact on GDP between 1.5 and 3.5 percent, potentially sending the economy back into a recession,” Snowe said.

“The question is, who are you fighting for,” Sen. Barbara Boxer, D-Calif., said before the vote. “Are you fighting for the people who make a billion dollars a year? That’s who the Republicans are fighting for, and they get so emotional about it. Or are you fighting for the middle class, the heart and soul of America.”

Republicans said the measure was all about Democratic posturing for the upcoming elections and would hurt the economy because boosting taxes on the wealthy will hinder them from hiring workers for their companies.

“Thank goodness it’s not going anywhere because it would be bad for the economy, the single worst thing we could do to the country,” Senate Minority Leader Mitch McConnell, R-Ky., said.

With Senate control at stake in November’s elections, Republicans were hoping that several Democrats seeking re-election would hurt their candidacies by having backed the Democratic package. The bill would dramatically boost the estate tax, which would be widely unpopular in farming, ranching and high cost-of-living states, and increase levies on dividends and capital gains, which are relied on by many elderly people.

“That’s what today’s votes are all about,” McConnell said in a thinly veiled warning to Democrats. “Showing the people who sent us here where we stand.”

The White House chimed in by reiterating its support for the Democratic plan.

“All sides agree on the need to extend the tax cuts for the middle class,” the White House wrote in a statement. “This legislation reflects that consensus and should not be held hostage while debating the merits of another tax cut for the wealthy.”

Under the Democratic measure, individuals earning over $200,000 and couples making at least $250,000 would see their top rates rise from 33 percent and 35 percent today to 36 percent and 39.6 percent in January.

Democrats argue that the well-off should contribute to efforts to contain federal deficits, while Republicans say many of those affected own businesses and would have a harder time hiring workers. The increase would affect 2.5 million households, or 2 percent of all 140.5 million tax returns, according to 2009 Internal Revenue Service statistics.

The Democratic bill would also boost the top tax rate paid by people who inherit estates to 55 percent, exempting the first $1 million in an estate’s value. The GOP measure would maintain today’s 35 percent top rate and would not tax the first $5.12 million of an estate’s value.

In fresh figures released this week by Republicans, Congress’ nonpartisan Joint Committee on Taxation estimated that the Democratic provision would affect 55,200 estates next year, compared with 3,600 who would face estate taxes under the GOP plan.

Democrats would impose top tax rates next year of 20 percent on dividends and capital gains, two sources of income enjoyed disproportionately by the wealthy. The GOP top rate would be 15 percent.

The GOP bill ignores some tax credits for low- and middle-income families that Democrats want to extend for college costs; for some low-income couples and large working families; and for families with children.

All were part of Obama’s economic 2009 stimulus bill. Democrats say those tax breaks were meant to be permanent but Republicans say they were only a short-term response to the recession.