But he acknowledged that on Sunday alone, in the final hours before the federal government’s quarantine rules took effect, some 5,000 American citizens flew back from China.

“If we had to actually quarantine all of those people instead of rely on self-quarantines, you can just imagine what that would do to available resources,” Mr. Cuccinelli said. “It would blow the doors off them.”

Even in states where no one has received a diagnosis of coronavirus, precautions were put in place.

In Texas, where Joint Base San Antonio was preparing for the possibility that it would house quarantined travelers from China, military leaders scheduled a town-hall meeting for Wednesday to answer community concerns about safety. Indiana health officials said they were monitoring a resident who federal authorities had said should be quarantined at home. And in Wheeling, W.Va., public health officials pulled someone out of an elementary school on Monday and placed the person and a family member in quarantine because they had just returned from Hong Kong.

“It’s going to be that time in the house together, watching a lot of movies, having family and friends bring the groceries over,” said Howard Gamble, the administrator of the Wheeling-Ohio County Health Department, which is checking in with the quarantined family by phone each day to make sure they are not developing any coronavirus symptoms.

Public health officials said the immediate threat to Americans remained low. But federal guidance for travelers has evolved quickly, creating a confusing patchwork of policies.