Perhaps no vote was as agonizing for Senator Bill Cassidy, the Louisiana Republican and medical doctor, than his vote to confirm Robert F. Kennedy Jr. as President Trump’s health secretary. Mr. Cassidy wondered aloud for days how Mr. Kennedy, the nation’s most vocal and powerful critic of vaccinations, might handle an infectious disease crisis.

Now, as a measles outbreak rages in West Texas, Mr. Cassidy has found out. It all comes down, he said, to “the gestalt.”

On Monday, days after the Texas outbreak killed an unvaccinated child, Mr. Cassidy, the chairman of the Senate Health Committee, was clipping down a Capitol corridor when he was asked about Mr. Kennedy. He pointed to a Fox News Digital opinion piece in which Mr. Kennedy advised parents to consult their doctors about vaccination, while calling it a “personal” decision.

“That Fox editorial was very much encouraging people to get vaccinated,” he said.

Reminded that Mr. Kennedy had described it as a personal choice, Mr. Cassidy thought for a moment. “If you want to like, parse it down to the line, you can say, ‘Discuss with your doctor,’” Mr. Cassidy said. “He also said, ‘We’re making vaccinations available. We’re doing this for vaccination. We’re doing that for vaccination.’ So if you take the gestalt of it, the gestalt was, ‘Let’s get vaccinated!’”

Mr. Cassidy’s assessment — that the whole of Mr. Kennedy’s message was more than the sum of its parts — reflects how the measles outbreak has put a spotlight on how Mr. Trump’s unorthodox choice to run the country’s top health agency has brought a once-fringe perspective into the political mainstream, creating discomfort for some Republicans.

As the founder and chairman of his nonprofit, Children’s Health Defense, and later as a presidential candidate, Mr. Kennedy has repeatedly downplayed the benefits of vaccination. He has also repeatedly suggested that the measles, mumps and rubella vaccine causes autism, despite extensive research that has found no link.

Since winning Trump’s nod to head the sprawling Department of Health and Human Services, Mr. Kennedy has walked a careful line on the issue. Some of his recent statements, in which he stops short of denouncing vaccines, have angered some of his supporters. But his less than full-throated endorsement of vaccination, and his promotion of alternative remedies to treat measles, have angered mainstream scientists who say the one proven way to prevent measles is the vaccine.

“This, I would say, is the barest of the bare minimum that one can do in the middle of a measles outbreak,” said Dr. Adam Ratner, a New York City pediatrician who just published a book, “Booster Shots,” that warns of a measles resurgence.

But Del Bigtree, Mr. Kennedy’s former communications director and one of his closest allies, said Mr. Kennedy was doing exactly what he said he would do: putting all options on the table and letting parents decide for themselves.

He used the word “balance” to describe Mr. Kennedy’s approach, and said the media was being “incredibly disingenuous and in some ways alarmist and dangerous by creating a panic over a death from measles.”

Asked about Mr. Cassidy’s “gestalt” remark, Andrew Nixon, a spokesman for the department, referred back to the Fox opinion piece. He said the health secretary’s comment could speak for itself: “Vaccines not only protect individual children from measles, but also contribute to community immunity, protecting those who are unable to be vaccinated due to medical reasons.”

Mr. Cassidy, a liver specialist, made his career in medicine treating uninsured patients as a doctor in Louisiana’s charity hospital system. He is a fierce proponent of vaccines.

But he is also facing a Republican primary challenger in 2026, and voting against Mr. Kennedy risked prompting Mr. Trump to endorse his opponent — and sparking a potential backlash among an increasingly vaccine-skeptical G.O.P. electorate.

Mr. Kennedy’s “medical freedom” movement, which he calls “Make America Healthy Again,” is now deeply entrenched in the Republican Party. The coronavirus pandemic turned many conservatives against vaccine mandates, even for children attending school. Around the country, nearly 1,000 candidates, nearly all Republican, ran for elective office in November with the backing of Stand for Health Freedom, a Florida nonprofit that has pushed to make it easier for parents to opt out of school vaccine requirements.

For Mr. Cassidy and other Republicans who were uneasy about Mr. Kennedy, the situation in West Texas is forcing a reckoning, said Whit Ayres, a Republican strategist who is also a member of Rotary International, an organization that has set a goal of ending polio by promoting vaccination around the world.

“His position on vaccines was exceedingly well known when he was nominated, and when he was confirmed by the United States Senate,” Mr. Ayers said. “Everybody, with their eyes open, knew that his positions could lead to a resurgence of measles.”

As vaccination rates have dropped around the country, public health experts have warned that measles would be the first infectious disease to come back. But the Texas measles outbreak cannot be blamed on Mr. Kennedy. The disease began spreading within the Mennonite community, an insular Christian group that settled in West Texas in the 1970s; many Mennonites are unvaccinated and vulnerable to the virus.

Mr. Kennedy minimized the situation in Texas during a Cabinet meeting with Mr. Trump last week, saying measles outbreaks in the United States are “not unusual.” His Fox opinion piece promoted the use of vitamin A, which studies have shown is useful in treating measles in malnourished children.

He followed up with a prerecorded Fox News interview that aired on Tuesday, in which he said parents and doctors should consider alternative approaches, including cod liver oil, for the treatment of measles. He also acknowledged that vaccines “do prevent infection.” But once again, Mr. Kennedy did not urge Americans to get vaccinated.

The Texas Department of Health issued a health alert on Jan. 23 reporting two cases of measles. Since then, nearly 160 people have contracted the illness and 22 have been hospitalized. The Centers for Disease Control and Prevention said Tuesday that it had sent some of its “disease detectives” to Texas to support local officials in the response.

By Wednesday, while Mr. Cassidy appeared satisfied with Mr. Kennedy’s handling of the matter, the senator was pushing another key health nominee on questions of measles, vaccines and autism.

He wanted to know whether Dr. Jay Bhattacharya, appearing before the Senate health committee for his confirmation hearing as Trump’s pick to lead the National Institutes of Health, intended to spend tax dollars on research into the discredited theory that vaccines cause autism. Mr. Cassidy had repeatedly, and unsuccessfully, tried to get Mr. Kennedy to reject that theory in his own confirmation hearing.

Dr. Bhattacharya told the senator he was “convinced” that there is no link between the measles vaccine and autism. But like Mr. Kennedy, he said he supported additional research, if only to assuage the fears of nervous parents.

Mr. Cassidy was incensed, saying the matter had already been settled by years of extensive research. New studies, he said, would waste taxpayer dollars and take away money from studies that might uncover the true causes of autism. He pounded his fist on the table.

“If we’re pissing away money over here,” he said with a wave of his hand, “that’s less money that we have to actually go after the true reason.”

And in any event, Mr. Cassidy said, further research would not change minds. “There’s people who disagree that the world is round,” he said, adding, “People still think Elvis is alive.”

To secure Mr. Cassidy’s vote last month, Mr. Kennedy made a series of concessions, which Mr. Cassidy outlined in a Senate floor speech. They included a pledge not to disband the committee of experts that advises the Centers for Disease Control and Prevention on vaccines, and to leave intact statements on the C.D.C.’s website saying that vaccines do not cause autism.

Mr. Kennedy also promised to have an “unprecedentedly close collaborative working relationship” with Mr. Cassidy, and to meet or speak with him “multiple times a month,” and to give Congress advance notice of any vaccine policy changes.

“I will carefully watch for any effort to wrongfully sow public fear about vaccines between confusing references of coincidence and anecdote,” Mr. Cassidy said then.

On his way into the Senate chamber on Monday, he said he thought Mr. Kennedy was doing a good job with the Texas response. “He’s handling it well,” the senator said. He was asked if he had spoken to Mr. Kennedy about the measles outbreak.

“We speak on a regular basis,” Mr. Cassidy said, adding: “Let’s leave it at that.”