The measure, which passed 234-188, is expected to die in the Senate, where Republicans have the votes to block it. Twenty Democrats voted against the House bill and three Republicans voted for it.
Despite the likely outcome, Senate Majority Leader Harry Reid may hold a vote on the House bill as early as Friday, Democratic aides said.
Most Democrats say Republicans were willing to jeopardize low tax rates for middle- and lower-income taxpayers to ensure low taxes for the wealthiest Americans.
The tax cuts were signed into law by former President George W. Bush in 2001 and 2003 and are set to expire December 31.
The Republicans want to continue to keep middle-income tax cuts hostage until it is combined with upper-income tax cuts, said Democratic Representative Sander Levin, head of the tax-writing panel in the House.
Republicans countered that allowing any tax rates to rise would threaten the economy, which is suffering from high unemployment rates.
The House action comes as congressional leaders and the Obama administration negotiate behind closed doors for a compromise that would allow Congress to extend tax rates before they expire at year's end.
The talks are ongoing and productive, but any reports that we are near a deal in the tax cut negotiations are inaccurate and premature, said White House press secretary Robert Gibbs.
On Capitol Hill, senior Democratic aides said they did not expect any significant progress until at least next week.
Another aide said many Democrats were worried the White House would not stand up to Republicans.
There's a growing concern that the White House won't fight hard enough for the middle class and will cave (on extending tax cuts for wealthier Americans) without getting much in return, other than perhaps a Senate vote on a stalled U.S.-Russian arms treaty, the aide said.
'THIS IS NONSENSE'
Democrats fear negotiations will go much as they did over the past two years on healthcare and the economic stimulus package, with President Barack Obama making concessions without getting much, if anything, in return from Republicans, the aide said.
The top House Republican blasted Thursday's vote on renewing only lower-tax rates as political maneuvering that would undermine the bipartisan talks.
This is nonsense, all right? The election was one month ago, said John Boehner, who is in line to become House speaker when Republicans take over in January.
U.S. Treasury Secretary Timothy Geithner and White House budget chief Jacob Lew met with two Republicans and two Democrats twice on Wednesday on the tax issue. Administration officials returned to the Capitol on Thursday.
The meeting ended with participants saying they were still working and would meet again in coming days.
Obama repeated his optimism that a deal could be reached. He has indicated a willingness to compromise in recent weeks, even as Republicans have dug in their heels.
I believe it will get resolved, Obama said at an unrelated event. That doesn't mean there may not be some posturing over the next several days.
If no agreement is reached, all tax-paying Americans could face higher bills next year, giving Republicans a chance to score politically by making tax cuts their priority when taking control of the House in January.
Finding common ground before then will be tricky.
EXTENSION LIKELY, DEMOCRATS SEEK CONCESSIONS
Many people, including some Democratic aides who asked not to be identified, believe a one-to-three year extension of all the Bush-era rates is the most likely scenario.
In exchange, Obama administration officials hope to win Republican consent to an extension of long-term unemployment insurance and to Senate ratification of the New START nuclear treaty with Russia.
They are also pushing to extend a tax credit for employers who hire workers previously unemployed and renewal of a credit for working individuals who make less than $75,000 a year, according to administration officials.
Any deal is likely to be coupled with an extension of business and individual tax breaks that have expired this year, including a research and development tax credit.
Division among Democrats has weakened their position. A few dozen conservative Democrats back the Republican stance that lower tax rates for all income groups should be extended.
They say raising taxes would hurt job growth and the economic recovery.
Most Democrats, however, say the United States cannot afford the tax cuts for the wealthy -- estimated at $700 billion over 10 years -- and that the wealthiest are unlikely to spend the extra cash in any event.
(Additional reporting by Jeff Mason, Matt Spetalnick and Thomas Ferraro; Editing by Stacey Joyce and Peter Cooney)