Republican suspicion of vaccines was building before the pandemic; when Donald J. Trump was running for president in 2016, he rejected established science by raising the debunked claims that vaccines cause autism. Now, some of the governors argue that given the country’s outsize divisions, and widespread suspicion of Washington, federal intervention would be counterproductive. It would be best, they say, to let state officials continue making the case that the vaccines are safe and effective, and to allow people to make decisions themselves.

“I’m trying to overcome resistance, but the president’s actions in a mandate hardens the resistance,” Gov. Asa Hutchinson, Republican of Arkansas, said Sunday on NBC’s “Meet the Press.” School mandates, he said, “have always come at the state level, never at the national level. And so this is an unprecedented assumption of federal mandate authority that really disrupts and divides the country.”

Dr. Jha said Mr. Biden had in fact done Republicans a favor.

“What the president does is he creates political cover for Republican leaders, who will scream loudly because it’s politically expedient,” he said. “But I think many of them are actually feeling relieved, because now they don’t have to do the hard work of convincing their constituents.”