“Of course I am concerned,” said Gov. Brian Sandoval, the Republican governor of Nevada, where about 300,000 people have gained Medicaid coverage. “I am someone who elected to expand Medicaid. That’s been very beneficial to my state, and I want to be sure those individuals can keep their coverage.”

“Governors are all in agreement,” said Gov. Terry McAuliffe of Virginia, a Democrat who is the chairman of the National Governors Association. “We do not want one single one of our citizens to lose access to quality health care. We are all unified on that. Actually, we want to expand, so everybody has access to quality health care.”

Mr. Trump brushed aside opinion polls suggesting that the 2010 health law was becoming somewhat more popular. “People hate it,” the president said, “but now they see that the end is coming and they’re saying, ‘Oh, maybe we love it.’ There’s nothing to love. It’s a disaster, folks.”

Because of the intricate procedures that govern budget legislation and the inherent complexity of health care, Republicans appear unlikely to undo the health law as quickly as they had hoped. Mr. Trump said Congress must tackle the Affordable Care Act before it can overhaul the tax code, also a high priority for Republicans. And those delays could slow work on other priorities like a trillion-dollar infrastructure push.