Similar concerns are playing out in other states. In Colorado, where Gov. Jared Polis said Tuesday he would allow his blanket stay-at-home order to evolve into an encouragement to be “safer at home,” these tentative steps have brought a mix of relief, confusion and worry.

“It seems reckless to just open willy-nilly when we have no way of knowing,” said Sherry Larkin, who runs a massage-therapy clinic in Denver.

And on Folly Island outside of Charleston, S.C., Mayor Tim Goodwin of Folly Beach was struggling with the implications of Mr. McMaster’s plan to begin rolling back mandatory closures of nonessential businesses and recreation areas.

On Tuesday, bicyclists far outnumbered cars; usually, on busy days in the spring and summer, cars from across the East Coast line up for miles to drive onto the island. The prospect of that returning now haunts Mr. Goodwin, as he imagines hundreds of visitors churning through his community. “People who want us to open the beach don’t want to admit that,” he said, “but that’s how this could get so much worse.”

And downtown Charleston was eerily quiet on Tuesday, bereft of the tourists, students and residents who typically crowd into restaurants, art galleries and retail shops. At M. Dumas and Sons, a 103-year-old store on King Street, Gary Flynn said the business was hanging on by serving a few clients by appointment, offering curbside pickup and taking online orders.

Mr. Flynn, 54, said he was concerned about its reputation as a longtime local retailer. “I can see negative blowback to stores. Here are people who’ve been told to stay home, but greedy retailers want people to come back out when it’s dangerous.”

The Southern governors moving ahead with easing restrictions, like Mr. Kemp and Mr. McMaster, were among the state leaders most reluctant to introduce them in the first place. They held off as most other states and some of their own cities put in place orders mandating that residents largely stay home.