A day after he announced the guidelines, the president took to Twitter to goad the Democratic governors of Michigan, Minnesota and Virginia to “liberate” their states from stay-at-home orders.

“I think elements of what they’ve done is too much,” Mr. Trump said, referring to the governors. He singled out Virginia Gov. Ralph Northam’s gun control efforts.

Washington state Gov. Jay Inslee, a Democrat who also has clashed with the president during the crisis, said Mr. Trump’s tweets about “liberating” states put millions at risk of contracting COVID-19.

“The president is fomenting domestic rebellion and spreading lies even while his own administration says the virus is real and is deadly,” Mr. Inslee said.

Mr. Trump denied he was fomenting “rebellion” and said the crisis was “too tough” for some leaders such as Mr. Inslee. He said the demonstrators “seem to be very responsible people to me. They’ve been treated a little bit rough.

“I just think that some of the governors have gotten carried away,” he told reporters. “I really believe somebody sitting in a boat in a lake should be OK.”

Protesters rallied Saturday in the state capitals of Texas and Maryland, both with Republican governors, calling on legislators to ease restrictions. Rallies also were held this weekend in Indiana, Nevada and Wisconsin.

Demonstrators in Michigan, Minnesota and North Carolina have also called for governors to allow people to get back to work. Michigan has been hit especially hard by layoffs. More than 1 million people there have their jobs in the past month.

The Trump campaign has targeted Michigan and Minnesota as key battlegrounds in the November elections. Mr. Trump won Michigan narrowly in 2016 and lost Minnesota to Democrat Hillary Clinton by 1.5 percentage points.

Virginia looks like a steeper hill for the president to climb. He lost the state by 5.3 percentage points four years ago.

In Pennsylvania, a state Mr. Trump won narrowly in 2016, about 1.3 million people or one-fifth of the work force have been thrown out of their jobs in the past four weeks.

The president said this month that Democrats “shouldn’t be al­lowed to win” the pres­i­dential race in November based solely on a pandemic that ruined the strong economy he had forged. Mr. Ayers, president of North Star Opinion Research, pointed out that the crisis has thrown the race into uncharted territory.

“If we can get the pandemic to the point where it no longer looks like a threat and the economy roars back, then obviously the president can run on his handling of the pandemic and the fact that it didn’t kill the economy,” Mr. Ayres said. “On the other hand, if we’re still struggling with massive unemployment come September and October, then it’s a completely different story.”

Presumptive Democratic presidential nominee Joseph R. Biden is making Mr. Trump’s response to the coronavirus outbreak a campaign issue, but the Trump campaign has shifted gears from the economy to Mr. Biden’s policy on China. Campaign officials say they will continue to hammer Mr. Biden through Election Day for being too cozy with Beijing and for Mr. Biden’s role in his son Hunter’s lucrative business deals in China.

Throughout the crisis, the president’s job approval rating hasn’t changed dramatically. At the end of February, his approval rating in the Real Clear Politics average of polls was 45.9%; on Friday, it was 45.7%.

“It’s been remarkably stable, even in the midst of a pandemic,” Mr. Ayres said. “The reason is that people have made up their minds about this president. Just as job approval did not go up as much as you would expect for a normal president with a booming economy and rock-bottom unemployment, so his job approval has not gone down as much as you would expect with a cratering economy and soaring unemployment. His job approval is driven far more by people’s judgment about his conduct and behavior in office than it is by any objective criteria.”

The president said this weekend that he expects the Democrats’ campaign to focus on criticism of his handling of the public health crisis. He pointed to a conference call that Vice President Mike Pence held Friday with Democratic senators, who criticized him for failing to provide specifics on increasing testing for coronavirus infection.

“He gave them everything that they would have wanted to hear in terms of gaining ground on the CoronaVirus, but nothing that anyone could have said, including ‘it’s over,’ could have made them happy, or even a little bit satisfied,” the president tweeted. “They were rude and nasty. This is their political playbook, and they will use it right up to the election on November 3rd. They will not change because they feel that this is the only way they can win. America will not be fooled!!!”

Timetables are not clear for any of the key battleground states to resume normal operations for work and education.

The Institute for Health Metrics and Evaluation’s model, which the White House uses to track infection rates, said some states could relax certain social distancing measures by May 4 if “robust containment strategies” are implemented to prevent a second wave of infections. Those states include Vermont, West Virginia, Montana and Hawaii, none of which is considered a toss-up in November.

The institute said other states, including the battlegrounds of Florida, Iowa and Georgia, “may need to wait until late June or early July” to ease social distancing.

Florida Gov. Ron DeSantis, a Republican and close ally of the president, said he will announce his plan this week for reopening the state. Mr. DeSantis said municipalities could reopen beaches and parks if they do so safely.

Texas Gov. Greg Abbott, a Republican, said state parks could reopen Monday and retail stores could resume business for pickup, delivery and mail order on Friday.

“We have demonstrated that we can corral the coronavirus,” Mr. Abbott said, though he acknowledged that the school year is finished.

Iowa is one of eight states that never ordered residents to stay at home. The others are Arkansas, Nebraska, North Dakota, Oklahoma, South Dakota, Utah and Wyoming.

“We’ve avoided the cataclysmic outcomes we’ve seen in other countries and other locations,” North Dakota Gov. Doug Burgum, a Republican, said last week.

Other states that appear to be readying for opening in phases sooner rather than later include Alabama, Arizona, Idaho, Mississippi, Ohio, Oklahoma, South Carolina and Tennessee.

Governors in both parties said their states won’t return to normal operations without assistance from the administration to expand testing

“The federal government cannot wipe its hands of this and say, ‘Oh, the states are responsible for testing,’” said New York Gov. Andrew Cuomo, a Democrat. “We cannot do it without federal help.”

In Illinois, it’s safe to say that Democratic Gov. J.B. Pritzker and the White House won’t be coordinating, at least for now. Mr. Pritzker said he has given up on receiving assistance from the federal government and announced that Illinois was “doing what we need to do despite” the president’s decisions.

White House deputy press secretary Judd Deere responded by saying, “Whether through ignorance or incompetence or a propensity to politicize everything, Gov. Pritzker is not being truthful with the people of Illinois when he says his state has not been provided resources from President Trump’s administration.”

The president said the administration has given states the capacity to ramp up testing and it’s governors’ responsibility to use more of that capacity.

“At some point in the not-too-distant future, we’re going to have our country back,” Mr. Trump said.