“We had two Republicans that went against us, which is very sad, I think. It’s very, very sad for them,” Mr. Trump said. “But I’m very, very happy with the result.”

Three crucial Republicans, Capito, Heller and Portman, are yes.

Senators Shelley Moore Capito of West Virginia, Dean Heller of Nevada and Rob Portman of Ohio, three Republicans who have expressed profound doubts about legislation to repeal and replace the Affordable Care Act, announced Tuesday they will vote to begin debate on the future of health care.

“Obamacare isn’t the answer, but doing nothing to try to solve the problems it has created isn’t the answer either. That is why I will vote to move forward and give us a chance to address the unworkable aspects of the law that have left many Nevadans — particularly those living in rural areas — with dwindling or no choices,” Mr. Heller said.

Ms. Capito said in a statement, “As this process advances on the Senate floor, I will continue to make decisions that are in the best interest of West Virginians. I remain committed to reforming our health care system while also addressing the concerns I have voiced for months. I will continue to push for policies that result in affordable health care coverage for West Virginians, including those who are in the Medicaid population and those struggling with drug addiction.”

Mr. Portman informed his state’s governor, John Kasich, that he too would vote on a procedural motion to take up a repeal bill.