"I think that reflects a growing sentiment in this country where that's going to tug against what the governors have to do," Gottlieb said on "Squawk Box." "They have tough decisions to face this month."
Late Wednesday, Musk lashed out, even dropping the F-bomb, on the electric vehicle maker's earnings call, saying that lockdowns meant to help slow the spread of the coronavirus are "fascist." He also said the orders amounted to "forcibly imprisoning people in their homes against all their constitutional rights."
A number of states across the country, such as Georgia, Colorado and Tennessee, has recently eased up on some of the coronavirus-related business restrictions. Other states, such as Ohio, have announced details of a phased reopening to begin in May.
For a complete list of state actions, see: How states are reopening businesses and lifting coronavirus restrictions
A significant majority of Americans continues to support restrictions on restaurants, large sporting events and in-person schooling until there is more widespread testing for Covid-19, according to a recent NPR/PBS NewsHour/Marist poll.
Despite the anger and outrage some Americans may feel, Gottlieb said, many states should continue with widespread mitigation efforts because of the number of new Covid-19 cases.
"We still face a pretty big epidemic in this country. The slope of the curve down isn't steep," the former Food and Drug Administration commissioner said. "We've plateaued but we haven't seen the declines across the country that we were expecting right now."
Gottlieb, a CNBC contributor who sits on the boards of Pfizer and biotech Illumina, said that only a few regions have demonstrated sustained reductions in new cases, including Ohio, Idaho and parts of the Northeast.
In states where cases are going up, Gottlieb said, governors should wait "a little longer" before relaxing restrictions. He said he understands it is a difficult decision due to the economic havoc wrought by the orders.
"I think the bigger risk right now is we reopen while we still have a lot of smoldering infection and so we never quite get rid of it It just continues to smolder all through the summer and then we face combustion in the fall," said Gottlieb.