“We’re going to do what we think is right — what I think is right — and that is try to open this economy,” Gov. Mike DeWine of Ohio said Sunday on NBC’s “Meet the Press,” “but do it very, very carefully so we don’t get a lot of people killed.”

In South Carolina, Gov. Henry McMaster, a Republican, said on Monday that department stores and some other retail businesses that had previously been deemed nonessential would be allowed to reopen on Tuesday, but they must abide by social distancing guidelines. People will also be able to gain access to public beaches on Tuesday.

Across the country, governors have been weighing steps toward lifting orders and reviving their stalled economies. A lack of sufficient widespread testing has been seen as one of the main obstacles.

At the White House’s coronavirus briefing on Monday, President Trump reacted dismissively to governors who said they had scrambled to access testing materials, such as nasal swabs and chemical reagents.

“Some states have far more capacity than they actually understand,” he said. “That is a complex subject, but some of the governors did not understand it.”