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If Republicans retake control of the Senate next year, Mr. McConnell said, he would support using budget reconciliation rules to repeal the health care law.

Doing so would prohibit Senate filibusters and require only 51 votes.

Mrs. Pelosi said she doubted that campaigning against the health care law would work, given that voters already are experiencing benefits from the Affordable Care Act and that some will be receiving refund checks in August.

“Some people say they’re already getting reduced rates for next year, thanks to the Affordable Care Act,” Mrs. Pelosi said. “Seniors are already paying less for prescription drugs. They may not know it, but it’s because of the Affordable Care Act, and we have to make sure that they do know it.”

The House is scheduled to vote again to overturn the law July 11, but that vote is almost certain to be largely symbolic with the Democrats in control of the Senate and the White House.