WASHINGTON — Facing intransigent Republican opposition, the Senate majority leader, Mitch McConnell, on Tuesday delayed a vote on legislation to repeal the Affordable Care Act, dealing another setback to Republicans’ seven-year effort to dismantle the health law and setting up a long, heated summer of health care battles.

Mr. McConnell faced resistance from across his conference, not only from the most moderate and conservative senators but from others as well. Had he pressed forward this week, he almost surely would have lacked the votes even to begin debate on the bill.

“We will not be on the bill this week, but we’re still working toward getting at least 50 people in a comfortable place,” said Mr. McConnell, who is known as a canny strategist but was forced to acknowledge on Tuesday that he had more work to do.

The delay pushes Senate consideration of the bill until after a planned recess for the Fourth of July, but it does not guarantee that Republican senators will come together. Opponents of the bill, including patient advocacy groups and medical organizations, plan to lobby senators in their home states next week. Senators are likely to be dogged by demonstrators. Democrats vowed to keep up the pressure, and some Republican senators have suggested that their votes will be difficult to win.