“They made it clear that he was categorically opposed to syringe exchange, period,” Mr. Clere said.

On March 4, county and state health officials got on a conference call with the New York State Department of Health. The agency explained how the spread of H.I.V. among drug users in New York City had been dramatically reduced years earlier.

“The first thing they said? ‘You need to have a clean needle exchange program,’” Ms. Combs, the county nurse, recalled.

But when the topic came up at a community meeting in Scott County the next week, Dr. Jennifer Walthall, the deputy state health commissioner, made it sound like an intervention of that kind was not possible, Ms. Combs said.

“She said, ‘Let’s focus on the mountains we can climb,’” Ms. Combs said.

On March 23, Mr. Pence was forced to address the topic head-on at a meeting in the governor’s office with state health officials and doctors from the Centers for Disease Control and Prevention.

“The governor looked to me and he looked to the C.D.C. and said, ‘What do we need to do to respond to this outbreak?’” Dr. Adams said.

He, for one, was no longer resistant. “The C.D.C. felt strongly, and I agreed, that providing syringes was the appropriate response, that this is an extraordinary situation that requires extraordinary measures.”

Mr. Pence found the science convincing, Dr. Adams said. But as the meeting concluded, no one was sure what the governor was going to do.