“We hope we can move forward and improve health care, not engage in another battle to take it away from people, because they will fail once again if they try,” said Senator Chuck Schumer of New York, the Democratic leader.
Senate Republicans already tried once this year to approve repeal legislation, an exercise that ended in defeat when Senator John McCain of Arizona gave a thumbs-down in July to kill that repeal proposal.
This time, Mr. McConnell and his fellow Republicans were trying to make one more attempt at passing a bill, and a deadline was fast approaching: They have only until the end of this week to pass a repeal bill using special budget rules that shield it from a Democratic filibuster.
Mr. McConnell could afford to lose only two of his members. But when he conceded defeat on Tuesday, three members of his conference had already publicly declared their opposition: Ms. Collins, Mr. McCain and Senator Rand Paul of Kentucky.
None of the three senators seemed likely to drop their opposition: Mr. McCain detested the partisan process used to push the bill, Ms. Collins had broad concerns about the legislation’s effects on health care, and Mr. Paul objected to the fundamental architecture of the legislation.
And other senators might have opposed it without doing so publicly. Senator Lisa Murkowski, Republican of Alaska, released a statement after the bill was pulled, decrying “a lousy process.”
“The U.S. Senate cannot get the text of a bill on a Sunday night, then proceed to a vote just days later, with only one hearing — and especially not on an issue that is intensely personal to all of us,” she wrote, without saying which way she would have voted.
Mr. Cassidy was blunt: “We don’t have the votes,” adding, “ Am I disappointed? Absolutely.”
But Mr. Graham predicted their repeal proposal would still pass — just at a later date, after Republicans tackle the issue of taxes, and when Republicans have more time to consider the repeal plan.
“There are 50 votes for the substance,” Mr. Graham said. “There are not 50 votes for the process.”
But that could be months away — if not years. The tax effort will likely occupy Congress through the remainder of this year, and likely into next. Lawmakers may not be able to revisit a partisan effort to repeal the Affordable Care Act until they tackle a budget plan for fiscal 2019, which would put the fight into the center of the midterm elections.
Earlier Tuesday, with little hope of success in the Senate, Mr. Trump expressed his displeasure.
“At some point there will be a repeal and replace, but we’ll see whether or not that point is now or will it be shortly thereafter,” he said at the White House. “But we are disappointed in certain so-called Republicans.”
“We’re a little frustrated that the Senate has not acted on a seminal promise,” Speaker Paul D. Ryan said.
Then he returned to talking up the goal of overhauling the tax code.