Even with the vote on Wednesday, the law is most certain to remain in place for now, as the the Democratic-controlled Senate doesn't plan to take up the repeal measure. President Obama would veto it if it clears the Senate.
Reps. Dan Boren of Oklahoma, Mike McIntyre of North Carolina and Mike Ross of Arkansas were the three Democrats who voted for repeal.
With the repeal vote behind them, House Republicans now must deliver on a second promise of last fall's campaign: proposing legislative alternatives to the Democrats' law. They will vote Thursday to pass a resolution instructing House committees to draft proposals they say will be more incremental than the Democrats' health overhaul.
Republicans' replacement plans remain vague and could easily fade as the party shifts toward proposals to create jobs. Any fresh health legislation is expected to stall in the Senate.
Pressed Wednesday for details of his party's health-care plans, House Speaker John Boehner described them as "common-sense reforms that bring down the cost of health insurance for the American people and expand access" to insurance.
Speaking on the House floor, Republicans called for enacting stronger curbs on medical-malpractice lawsuits and letting insurers sell policies across state lines. Yet they also suggested they favored keeping elements of the Democrats' law, including a provision allowing children to stay on their parents' health-insurance policies until age 26 and a ban on insurers denying coverage due to pre-existing conditions.
Democrats said the Republicans' ideas were marginal and would do little to solve the health system's problems. "It's easy to say you're against something. It is much harder to come up with solutions," said Rep. Susan Davis (D., Calif.). "It's irresponsible to repeal without a plan to fix the issues in our health-care system."
Republicans are moving decisively against the law because they sense strong public support among their backers and activists to do so. They believe they succeeded in the 2010 midterm election in portraying the overhaul as a metaphor for an overreliance on big-government solutions, and now have a mandate to act.
Among Republicans, 77% favor repealing and eliminating the law, according to a Wall Street Journal-NBC News Poll released Wednesday.
Among the public overall, the new poll found 46% of respondents opposed repealing and eliminating the law, while 45% favored that outcome. At the same time, health care ranked third on a list of most important economic issues, well behind unemployment and just behind the federal budget deficit.
Some Democrats questioned why Republicans were trying to undo the bill if they support its goals.
"They want to repeal the bill but they still want to give it a big hug and embrace," said Rep. Anthony Weiner (D., N.Y.).
"There are some things in the new law that are worth keeping, but until you sweep away the bad things, you cannot begin to work on the good things," said Rep. Joe Barton (R., Texas).
The resolution to be passed by Republicans Thursday calls for House committees to draft legislation that would, among other things, give states greater flexibility to administer Medicaid programs and prohibit taxpayer funding of abortions, which Democrats contend their law already does.
The Energy and Commerce Committee, in a memo outlining its priorities, said this week it would work to recapture the law's cuts to Medicare spending and funnel them back into the insurance program for the elderly. The law, designed to expand insurance to 32 million Americans, shaves more than $400 billion in Medicare payments over a decade.