She is a first-term governor and rising star in the Democratic Party, a frequent critic of the Trump administration for its handling of the coronavirus health crisis and a prominent foil of the president’s in the heated debate over when to reopen the nation for business.

Now the governor, Gretchen Whitmer of Michigan, has also become a prime target in the growing partisan storm over stay-at-home orders during the outbreak, which was highlighted on Wednesday by a raucous protest at the state capital, followed by Mr. Trump’s call on Friday to his followers to “Liberate Michigan.’’

The debate over how soon to loosen restrictions on businesses and workers has moved from the hands of health experts to become an increasingly political fight over costs to the economy, which Mr. Trump sees as crucial to his re-election.

Ms. Whitmer, a potential vice-presidential pick, has stirred Republican fears that her growing popularity will help Democrats carry the battleground state of Michigan in November, whether or not she is on the ticket. “I think it’s impossible to look at this and not feel there’s a lot of partisanship going on as it relates to Governor Whitmer,’’ said Debbie Stabenow, a Democrat and Michigan’s senior senator.

The traffic-snarling protest on Wednesday that drew a few thousand people to Lansing, Mich., including many flying Tea Party flags and Trump 2020 flags, was nominally called to oppose Ms. Whitmer’s latest stay-at-home order, one of the strictest in the nation. But the gathering, like similar ones held in the electoral battleground states of Ohio, Minnesota and North Carolina, was also the clearest sign yet of a simmering ideological movement on the right resisting government mandates over the virus.

“It felt a lot more like a political rally than a statement about the stay-home order,’’ Ms. Whitmer said in an interview the next day.

Mr. Trump has been insulting and condescending toward Ms. Whitmer, calling her “Half Whitmer” and “the woman in Michigan.” Asked on Thursday at the White House if the protesters in Michigan should listen to their governor, Mr. Trump replied: “I think they listen to me. They seem to be protesters that like me and respect this opinion.”

On Friday, he kept up the pressure, tweeting “Liberate Michigan’’ along with similar tweets for Virginia and Minnesota, which also have Democratic governors. His tweets came moments after a Fox News broadcast of protesters in state capitals violating social-distancing rules.

But unlike those two other Democratic governors, Ms. Whitmer is a Republican target because, among other reasons, she is in widely seen as in contention to be Joseph R. Biden’s running mate this fall.

In the interview, Ms. Whitmer said she has spoken recently with Mr. Biden about managing the pandemic.

“He’s called to check in a few times just to see what’s going on in Michigan, to ask thoughtful questions about what we need, but you know, we haven’t had that conversation,’’ she said, referring to Mr. Biden’s hunt for a vice-presidential candidate.

Asked if she thought she was prepared to be vice president, Ms. Whitmer, a former Democratic leader of the State Senate, who was known for her careful political timing under Republican majorities, deflected.

“Honestly every ounce of energy I have is being put into protecting people and saving lives in Michigan,’’ she said. “I’m not thinking about politics. I’m not. I don’t have energy for any of that right now.’’

The protests at state capitals in recent days had the feel of early Tea Party rallies in 2009, with far-right conservatives taking a lead role and more cautious elected Republicans keeping their distance. While polling shows that overwhelming majorities of voters are chiefly concerned about the public health threat, it also indicates that the most conservative Americans are more likely to be irked by the idea that their local economy might stay closed for a long time.

In a survey released Thursday by the Pew Research Center, very conservative Americans were twice as likely as others to worry that businesses would reopen too slowly. Yet very conservative voters were also unlikely to be too concerned about the virus’s economic impact. A Fox News poll out last week found that the most conservative voters tended to express less worry than others that the shutdown could send the economy into recession.

These ideas may seem hard to square, but the rhetoric of protest organizers and hard-line media personalities provides at least a partial explanation: very conservative voters are more likely to allude to a sense of outrage over having their public conduct restricted, rather than caution about the economic implications of the shutdown.

John Anzalone, Ms. Whitmer’s pollster and a Michigan native, said the protests were not “reflective of real people” in a state where most are more worried that they or a family member will get sick than the they are about the economic impact of stay-at-home orders.

But Mr. Anzalone said the right would only grow louder the longer the restrictions are in place. “She is reflective of the pressure other governors are going to get,” he said.

In Michigan, the state with the third-highest number of deaths from Covid-19, Ms. Whitmer imposed some of the country’s most severe restrictions on April 9, including a ban on travel to vacation homes and the sale in large stores of paint, garden supplies and furniture.

Her order was mocked on social media with posts of seed aisles cordoned off, criticisms that morphed into misinformation that was amplified by national Republican figures, including Senator Ted Cruz of Texas.

Republican lawmakers in Michigan, who had backed an earlier, less restrictive executive order, blasted the governor. They moved to strip Ms. Whitmer’s power to declare a state of emergency under a 1945 law.

“Here’s my message today: OUR Governor IS DESTROYING OUR HEALTH BY KILLING OUR LIVELIHOODS!” the State Senate majority leader, Mike Shirkey, tweeted this month.

On Monday, the governor accused the DeVos family, a wealthy and powerful force in Michigan Republican politics, of a role in the protest at the Capitol. Without naming Betsy DeVos, President Trump’s education secretary, Ms. Whitmer said it was “really inappropriate for a sitting member of the United States president’s cabinet to be waging political attacks on any governor, but obviously me here at home.”

One of the named hosts of the protest was the Michigan Freedom Fund, a conservative group with ties to the DeVos family. Its executive director, Tony Daunt, said the group’s only role was to promote the event on Facebook, at a cost of $250 to be listed as a co-host.

Mr. Daunt said Ms. Whitmer’s initial, less restrictive stay-at-home orders in March had bipartisan support, but she lost credibility with her tighter restrictions, which he called “dismissive” of people’s concerns about lost livelihoods.

Her frequent appearances on national TV, including the “Daily Show” with Trevor Noah and the Rachel Maddow show on MSNBC on Thursday, also set off conservatives. Mr. Daunt accused Ms. Whitmer of putting more “focus on the Biden veepstakes, as opposed to handling the crisis here in our own backyard.”

The governor called the charge “baloney,’’ defending her television appearances as chances to educate viewers about the virus, which attract offers of help for Michigan. “You know what, it would be wrong not to do everything I could on both those fronts,’’ she said. But even some Democrats in the state have raised an eyebrow at her ubiquity on national television.

Few other states outside the northeast have been as hard hit by the virus as Michigan, which recorded 2,226 deaths as of Friday, and where the intersection of race, presidential politics and Ms. Whitmer’s vice-presidential prospects have turned the perennial battleground into a political tinderbox.

With the outbreak concentrated in heavily black and Democratic Detroit, the virus was already threatening to exacerbate the widening political divide between rural and urban Michigan. For decades, Democrats enjoyed strength with working-class whites in rural Michigan. But as in much of the country, those voters have drifted to the G.O.P. over the last decade. Now, even when Democrats win statewide, as they did when Ms. Whitmer succeeded a Republican in 2018, they do so by piling up large margins in metropolitan areas and losing many of the less-populated counties where they once were strong.

And the images of nearly all-white protesters demanding the governor relax restrictions while hoisting Trump signs and Confederate battle flags, as the virus disproportionately impacts Michigan’s black residents, will only further cleave the state.

Less noticed is another flash point. A number of white Michiganders — many of them affluent but some firmly in the middle-class — have summer homes “up north,” as the sprawling upper tier of the state’s lower peninsula is called. Ms. Whitmer’s order that people not travel between their residences — meant to protect rural towns and rural hospitals from being overwhelmed with the virus — has particularly inflamed those state residents eager to get to their cottages.

Of course, for the heavily black work force in and around Detroit that can’t retreat to a vacation home, such an inconvenience is trifling by comparison. Many of these workers plays critical roles running the region’s vitally needed grocery stores, pharmacies and busses.

“Black people’s lives haven’t changed in many ways because everyday was always a grind to survive,” said Adam Hollier, a state senator from Detroit, adding that “grocery store clerk, home health care, bus drivers, sanitation, custodial staff — the people who are often deemed most replaceable are the ones we actually can’t live without.”