Washington (CNN) -- The House of Representatives voted to repeal the Obama administration's signature health-care legislation Wednesday evening, a vote the newly elected Republican majority called a fulfillment of their No. 1 campaign promise.

The bill, dubbed the "Repealing the Job-Killing Health Care Law Act," passed 245-189. Three Democrats joined a unanimous Republican caucus on the vote.

The legislation is unlikely to make it past the Democratic-controlled Senate, where Majority Leader Harry Reid has said he won't bring it to the floor for a vote. And even if it did, it would face a certain veto by President Barack Obama. But Rep. Mike Pence, a leading GOP conservative, dismissed Democratic criticism that Wednesday's vote was a "gimmick."

"We have another term for it on our side of the aisle: It's a promise kept," he said. "And House Republicans are here to stand with the American people and say with one voice, 'We can do better.' We can do better than their government takeover of health care."

Republicans have not presented an alternative bill to replace the Patient Protection and Affordable Care Act, which passed in 2010 over their unanimous opposition. House Speaker John Boehner said Republicans will ask congressional committees to come up with "common-sense reforms" that will widen coverage while bringing down costs, but told reporters no "artificial deadlines" were needed.

Most Republicans have acknowledged the virtual impossibility of an outright repeal, but have said they will try to cut funding to portions of the measure or eliminate specific provisions in the months ahead.

The nearly $900 billion health-care law passed Congress in 2010 over unanimous Republican opposition. It is estimated to extend health coverage to 32 million Americans when fully implemented -- the biggest expansion of federal health care guarantees since the creation of Medicare and Medicaid.

It bars health insurers from denying coverage for pre-existing conditions, eliminates lifetime caps on coverage and allows families to keep children on their policies until age 26.

It requires Americans to obtain health insurance, but also provides subsidies for small businesses and individuals to obtain that coverage. It requires insurers to cover preventive care, and sets up an independent appeals process for people who feel their claims were unfairly denied.

Rep. Peter DeFazio, D-Oregon, said the bill would bring back the "bad old days" for many Americans.

"Let's talk about the insurance industry pre-reform. They could cancel your policy if you got sick, even though you had been paying the premiums for years. They could refuse to sell you a policy if they don't like the way you look or you had a minor health problem. We changed that," he said.

Most Republicans argued the health-care law, passed over their unanimous opposition, will hamper prospects for long-term economic growth while doing little to slow spiraling medical costs -- and many of them, including House Majority Leader Eric Cantor, argued the law harms American freedoms.

"This legislation we seek to repeal is rooted in having federal bureaucrats come between patients and their doctors," Cantor said.

But Democrats defended the law, with some sharply criticizing Republican arguments as bogus.

"You know, I want to just advise people watching at home playing that now-popular drinking game of 'You take a shot whenever Republicans say something that's not true:' Please assign a designated driver," said Rep. Anthony Weiner, D-New York. "This is going to be a long afternoon."

Not all Democrats opposed the repeal effort, however. Reps. Dan Boren of Oklahoma, Mike McIntyre of North Carolina and Mike Ross of Arkansas cast their lot with the Republicans.

Republicans also are attempting to get the legislation struck down by federal courts. A federal judge in Florida on Wednesday allowed Ohio, Kansas, Wyoming, Wisconsin, Maine and Iowa to join a lawsuit filed there last year, bringing the total number of states in that case to 26. Virginia is pursuing a separate lawsuit, and Oklahoma says it will bring suit as well.

A federal judge in Virginia ruled in December that the individual mandate provision is unconstitutional, but two other judges have found the mandate passes constitutional scrutiny.

Democrats have warned that a reversal would be catastrophic to small businesses and unfair to millions of Americans depending on the reform to guarantee coverage. The Department of Health and Human Services released an analysis Tuesday morning warning that almost 130 million nonelderly Americans with pre-existing conditions would be at risk of losing their insurance without the guarantees provided by the legislation.

And the nonpartisan Congressional Budget Office says repealing the measure would cost up to $230 billion by 2021. Republicans dispute that figure, but they have nonetheless exempted the bill from House rules that forbid legislation from adding to the federal debt.

In the Senate, Reid has dismissed the GOP repeal effort as "partisan grandstanding." But Cantor, whose fellow Republicans have filibustered large numbers of Democratic bills in the upper chamber, demanded the Senate take up the measure.

"The American people deserve a full hearing. They deserve to see this legislation go to the Senate for a full vote," Cantor said. "The Senate ought not be a place that legislation goes into a dead end."

Senate Minority Leader Mitch McConnell of Kentucky said after the vote that the Senate would vote on the House measure.

"The Democratic leadership in the Senate doesn't want to vote on this bill, but I assure you, we will," McConnell said. "We should repeal this law and focus on common sense steps that actually lower costs and encourage private sector job creation."

President Barack Obama and other top Democrats have continue to express strong support for the law, which is widely viewed as the president's signature domestic achievement.

"I'm willing and eager to work with both Democrats and Republicans to improve the Affordable Care Act. But we can't go backward," Obama said in a statement Tuesday.

Leading members of both parties agree on the need for a limited number of changes to the law. Specifically, they have expressed concern about a rule, scheduled to take effect in 2012, requiring businesses to issue 1099 tax forms to any individual or corporation from which they purchase more than $600 in goods or services in a year.

"A lot of our small businesses came to me (after the health care overhaul passed) and said, 'There's a lot of paperwork I now have to fill out,' " Sen. Kirsten Gillibrand, D-New York, said Sunday on CBS's "Face the Nation." "We can change that. That's something we can absolutely agree on."

The Budget Office analysis indicates Republicans may have trouble moving ahead with their long-term strategy of cutting funding to the law. The measure includes $106 billion in new spending authorizations that Congress will eventually need to appropriate, according to Budget Office Director Doug Elmendorf. But $86 billion of those authorizations cover politically sensitive programs that were in existence before the passage of health care reform.

Funding for certain key provisions -- such as the law's Medicaid expansion and the extension of new insurance subsidies -- cannot be cut without a direct repeal vote.

CNN's Alan Silverleib, Deirdre Walsh, and Tom Cohen contributed to this report.