WASHINGTON — Waging old battles with new zeal, the House passed a bill on Wednesday to repeal President Obama’s health care overhaul law less than two weeks after the ­Supreme Court upheld its major provisions as constitutional.

The bill, which was approved by a vote of 244 to 185, has no chance of approval in the Senate and would face a veto from Obama if it ever got to him. But the House debate exposed the depth of passion over efforts to remake the health care system and suggested that the fight will continue next year, regardless of who wins the November elections for president and Congress.

House Republican leaders detest the 2010 law and see it as a winning political issue for them. And they wanted to placate freshman Republicans such as Ben Quayle of Arizona, who described repeal of the health care law as a way to protect constituents from ‘‘the tyranny of government overreach.’’

The House has voted more than 30 times to repeal part or all of the 2010 law or to choke off funds needed for various provisions, including coverage of more than 30 million uninsured people.

Democrats said the House was wasting time better spent trying to create jobs.

Representative Marsha Blackburn, a Tennessee Republican, said: ‘‘We’re going to keep at it until we get this legislation off the books. It was a bad bill, it has become a bad law.’’

In two days of House debate this week, both parties recycled talking points with minor changes to take account of the recent Supreme Court decision.

Democrats said the ruling vindicated their policies, including a requirement for most Americans to have health insurance, starting in 2014. And they said Obama needed to do a better job of defending the law,.

The Supreme Court ruling fired up Republicans because, they said, it confirmed their argument that the law would impose a tax, not just a penalty, on people without insurance.

‘‘The court has spoken,’’ said Representative Sandy Adams, Republican of Florida. “ ‘Obamacare’ is a tax.’’

Nancy Pelosi of California, the House Democratic leader, described the law as one of the Democrats’ greatest achievements, making health care ‘‘a right, not a privilege, for all Americans.’’ But Republicans still seeth over how the law was adopted, without any Republican votes.

Representative John Fleming, Republican of Louisiana, said the health law ‘‘never would have gotten passed’’ if the penalty for violating the individual mandate had been openly acknowledged and advertised as a tax.

Democrats said the attacks were overblown and quoted statements by Mitt Romney supporting an individual mandate as part of the health plan adopted in Massachusetts in 2006, when he was governor.

Representative Sander M. Levin of Michigan, the senior Democrat on the Ways and Means Committee, said that ‘‘almost no one’’ would pay the federal penalty.

‘‘The Congressional Budget Office estimates that only 1.4 percent of Americans will pay anything for refusing to purchase insurance,’’ Levin said. ‘‘That is just about identical to the percent of people in Massachusetts who have paid the penalty under Governor Romney’s health care law.’’

Levin said the federal law should be viewed as a tax cut for middle-income people because it provides tax credits to help them pay premiums for private health insurance.

Romney, the Republicans’ likely presidential nominee, says he would take immediate action to roll back the federal law if he wins the White House.