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 it as constitutional.

The bill was approved by a vote of 244 to 185, with five Democrats supporting repeal.

It has no chance of approval in the Senate and would face a veto from Mr. 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 would continue next year, regardless of who wins the November elections for president and Congress.

House Republican leaders had many reasons for voting on another repeal bill. They detest the 2010 law. They see it as a winning issue for them. And they wanted to placate freshman Republicans like Representative Ben Quayle of Arizona, who described repeal 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 money needed for various provisions, including coverage of more than 30 million uninsured people.