Trump and Allies Push Toward Reopening Economy. But Governors Urge Caution.

“It just reflects the flexibility a state needs,” Mr. Hutchinson, a Republican, said.

He noted that the hospitalization rate in Arkansas had been low so far. The state, with a population

of 3 million, has reported 1,280 cases and 27 deaths through Sunday.

Arkansas has called for strict social distancing, but has allowed businesses to stay open and people to go to work. “That’s the important balance that we have in our state,” he added. “If we need to do more, we will do more.”

Dr. Anthony S. Fauci, the director of the National Institute of Allergy and Infectious Diseases, said on Sunday that reopening the country would not be an “all or none” proposition. Dr. Fauci said in an interview with CNN that restrictions must be lifted in a gradual manner to prevent a resurgence of cases. Models show that lifting all social-distancing measures at once nationally may set the stage for a rebound sometime in July.

“If all of a sudden we decide, ‘OK, it’s May, whatever, and we just turn the switch on, that could be a real problem,” Dr. Fauci said.

He said that governors would need to manage a “rolling re-entry,” guided by testing results and local risk levels. “I think it could probably start, at least in some ways, maybe next month,” he said on the network’s “State of the Union” program. But he added, “Don’t hold me to it.”