McMaster also loosened restrictions on public access to South Carolina beaches and waterways, leaving it up to local jurisdictions.

The moves come even as the state's coronavirus outbreak continues to grow, Mayor Stephen Benjamin of Columbia pointed out Tuesday. The Democratic mayor told CNN that he’s been “operating on the other side” of the governor’s approach, focusing on data indicators, “not arbitrary dates.”

“When you should go back to business is when you have some true indicators over two weeks that show a deceleration of the pandemic," Benjamin said, referring to one of the White House's criteria in its multi-phase guidelines for reopening state economies.

“We need more testing. We need more data, and then we can decide how we go back into business," Benjamin continued. "But the challenge we're seeing is in places like Florida and Georgia, and yes, even here in South Carolina, is there is not that dialogue that is data-focused.”

As Benjamin alluded to, Georgia's Republican governor, Brian Kemp, has been even bolder in his moves to reopen the state's businesses shuttered by the coronavirus pandemic. Bowling alleys, gyms, tattoo parlors and hair and nail salons will be allowed to reopen beginning Friday, as long as business owners adhere to social-distancing and hygiene guidelines. Starting next week, movie theaters can reopen and restaurants will be allowed to return to limited dine-in service.

When pressed on Kemp's announcement during Tuesday's White House briefing, Dr. Deborah Birx, the coronavirus task force’s response coordinator, refrained from supporting the governor's blanket approach to reopening the businesses. She said she had made it clear that these decisions should be data-based, and that communication among governors and mayors was key to ensuring that the public "is completely protected."

"I believe people in Atlanta would understand that if their cases are not going down, that they need to continue to do everything that we said — social distancing, washing your hands, wearing a mask in public," Birx said. "So, if there is a way people can social-distance and do those things, then they can do those things. I don't know how, but people are very creative. So, I'm not going to prejudge, but we have told people very clearly and the president‘s guidelines made it very clear about the expectation of Phase One."

Trump added that he would be speaking to Kemp "in a little while," to ask him questions like, "Are they doing testing before they go in?"

Democratic mayors in the state have condemned the governor’s orders. Mayor Kelly Girtz of Athens-Clarke County, Ga., told CNN Tuesday that he was urging his constituents not to follow the governor’s advice for reopening.

“I’m exhorting everybody in this community to continue to shelter in place. Do not reopen at this point. It’s not the time to do it,” Girtz said. “It’s like telling the quarterback, ‘We don’t have a helmet for you, we don’t have pads, but get out there on the field and just try not to get sacked.”

Savannah Mayor Van Johnson noted on CNN Monday that the city had yet to see a 14-day decline as the virus continues to infect and kill residents throughout the state.

“I’m beyond disturbed,” he said. “In my mind, this is reckless, it’s premature and it’s dangerous. It’s not based in any type of science of best practices.”

Other Republican governors in states like Texas and Florida are beginning to issue reopening plans, setting off similar alarms among local Democrats, who worry the moves may be too ambitious.

St. Petersburg Mayor Rick Kriseman and Tampa Mayor Jane Castor held a joint virtual news conference on Monday to call on Florida Gov. Ron DeSantis to listen to the science and to be aware of how the virus is affecting different regions across the state. Kriseman said he would rather the state take more time before reopening because in the long-term, Florida will be “better off.”

Added Castor: “If we go out too quickly, and we end up further back than where we started, I mean, can you imagine what that will do? ... I just hope and pray that we’re not going to be used as the canary in the coal mine here.”

Local leaders in Texas echoed the same warnings after Gov. Greg Abbott announced plans last week to loosen surgery restrictions at medical facilities, allow retail stores to provide product pickups and reopen state parks.

When it comes to coronavirus testing, "we’re not there yet," Mayor Harry LaRosiliere of Plano, Texas, said in an interview with WFAA, a local ABC affiliate. "I think, to me, that’s the crucial turning point before things can move forward”