Wisconsin had barely finished its fight over whether to hold an election in the middle of the coronavirus pandemic before America’s foremost battleground state began another political brawl over the pandemic itself.

Officials from both parties rushed to familiar corners this week, with Democrats rallying behind Gov. Tony Evers’s decision to extend the state’s stay-home ordinance through May 26, while Republicans are stoking anger over what they depict as an assault on civil liberties.

Wisconsin’s decade-long partisan war will once again be on display Friday, as right-wing protesters prepare to mass outside the State Capitol in Madison to assail Mr. Evers and the restrictions he put in place to curb the spread of the virus. Thousands of people have indicated on Facebook that they will attend, making it potentially the largest gathering so far in a nationwide series of protests against stay-at-home restrictions.

Republicans, in need of a show of force after badly losing a State Supreme Court contest this month, have sued Mr. Evers to block the extension, discussed removing his public health secretary and, in recent days, amplified protesters’ calls to reopen the state while covertly helping to coordinate the Madison rally and other satellite gatherings across the state.

The planned protests on Friday, along with smaller events last weekend, have focused attention on the thorny issues governors face as they grapple with the decision over when to ease restrictions, with President Trump alternately encouraging protests calling for states to reopen and warning about the health risks of doing so. And in Wisconsin, a state critical to both Mr. Trump and the presumptive Democratic nominee, former Vice President Joseph R. Biden Jr., the demonstrations serve as a stand-in for the general election battle to come.

“This seems to have become a proxy war for the state Republican Party and it does have a zombie Tea Party feel to it,” said Charlie Sykes, a longtime conservative talk radio host in Milwaukee who left the airwaves at the end of 2016 and has since turned against Trump-era Republicans. “This will energize them to think that they’re back on the offensive. They didn’t miss a beat from losing that Supreme Court election and this all seems about mobilizing and firing up the base.”

The legal challenge to Mr. Evers’s extension follows a similar effort in early April, when Republicans led by Robin Vos, the speaker of the Wisconsin State Assembly, successfully petitioned the State Supreme Court to block the governor’s order to move the election date as well as an effort to switch to an all-mail election.

Mr. Vos, in an interview, portrayed the uprising against Mr. Evers as a broad response among Wisconsinites that crossed party lines. “It’s not just Republicans,” he said. “It’s a whole lot of people who own a small businesses and they’re unemployed and there’s no reason they can’t work.”

Vicki McKenna, a conservative talk radio host who has promoted the rallies on her program, said she hoped they inspired county sheriffs and local public health departments to defy the governor’s coronavirus orders.

“You go to central and northern Wisconsin, you have folks who are looking at Milwaukee and saying, ‘We understand that they need help, but why do we have to sacrifice our entire livelihood for them?’” she said.

While deep anger is growing on the right, there is some evidence that the Republican stance on the coronavirus is repelling voters Mr. Trump will need to carry the state in November.

Future Now Fund, a progressive organization that focuses on state legislative races, found in a study that in this month’s State Supreme Court race, Wisconsin counties with higher coronavirus infection rates saw larger shifts to the liberal candidate than did counties with lower rates. The shifts occurred in both urban and rural counties.

“Experiencing coronavirus can push people beyond their tribal lane to a different engagement with politics,” said Daniel Squadron, the co-founder and executive director of Future Now Fund.

And Democrats’ private polling in Wisconsin conducted after the election but before the protests began found 72 percent of Wisconsinites approved of how Mr. Evers has handled the coronavirus response. The same poll found Mr. Trump’s coronavirus job approval in the state was 51 percent.

“They can try to do this ‘We’re going to play to our base’ thing,” said Sachin Chheda, a Milwaukee Democratic operative who ran the Supreme Court campaign for the victorious liberal candidate, Jill Karofsky. “It’s bad politics. They might get some short-term wins, but it isn’t going to help them win in November.”

The organizers of the Madison rally and the two others held last weekend have gone to great lengths to describe themselves and their events as nonpolitical, despite ample evidence that the state’s Republican leadership is intricately involved. They are also trying to prevent the gatherings from becoming a platform for other conservative causes, or from appearing like de facto Trump campaign rallies.

Brian Westrate, the treasurer of the Republican Party of Wisconsin, posted to a private Facebook group for organizers and some attendees of the Madison rally, asking people not to bring emblems of causes other than resisting the stay-at-home order.

“Ok folks, I implore you, please leave Confederate flags and/or AR15s, AK47s, or any other long guns at home,” Mr. Westrate wrote. “I well understand that the Confederacy was more about states rights than slavery. But that does not change the truth of how we should try to control the optics during the event.”

In an interview, Mr. Westrate acknowledged writing the post and said it may be futile to ask the rally participants to limit the variety of their political motivations.

“Ideally, people should leave Trump stuff at home,” he said. “But you can’t hold a rally in favor of the First Amendment and then become over-draconian in terms of telling people how to dress.”

At two rallies last weekend, in the conservative Milwaukee suburb of Brookfield and the rural town of Mosinee, protesters carried Confederate flags, waved Trump signs and toted firearms, according to attendees and news photographs of the gatherings.

Cory Tomczyk, who hosted the Mosinee rally on the grounds of his industrial recycling company — which provides raw materials to companies making paper products — said he hoped the protests served as a conservative resistance in the same way that the state’s liberals were galvanized by Gov. Scott Walker’s 2011 move to end collective bargaining rights for the state’s public employees.

“People have this image in their head that they’re going to make it look like the protest for Act 10,” Mr. Tomczyk said, referring to the uprising against Mr. Walker’s labor law. “I don’t know if it will look like that, but I hope it will.”

With Ms. McKenna and others in the state’s powerful network of conservative talk radio hosts promoting the rally daily, the event will likely draw scores of Republican elected officials on hand to lend their support, but perhaps not dominating the stage.

Shae Sortwell, a Republican state representative from Manitowoc County, said his caucus’s G.O.P. leadership suggested members not speak at the rally to try to make sure it comes across as “a citizen-led effort.” Mr. Sortwell said he had no qualms about attending the rally.

“Do we want to take away what people have to live for in the sole pursuit of one singular goal of additional survival,” Mr. Sortwell said. “Is it safe, is it unsafe? I don’t know.”

Adrianne Melby, a social media marketer for a Racine County chiropractic firm who is one of the planners of the Madison rally, said organizers had sought to portray the event as homegrown and apolitical. She said they turned down a donor’s offer to help pay for the event, though Ms. Melby declined to say who made the offer.

Wisconsin’s State Capitol Police on Monday denied the Madison group’s official permit request. Mr. Evers’s spokeswoman, Melissa Baldauff, said there would not be an effort to stop people from gathering outside the Capitol — they just would not be allowed inside the building.

Mayor Satya Rhodes-Conway of Madison said she would not use the city’s police department to force protesters to disperse.

“All indications are that these are manufactured protests,” Ms. Rhodes-Conway said. “They are seeking attention. I think they are getting more attention than they deserve.”

One prominent dissenter among the state’s Republicans is Senator Ron Johnson, who rose from being the chief executive of a plastic manufacturer to winning a Senate seat in the 2010 Tea Party wave. Mr. Johnson said he wouldn’t criticize the governor’s stewardship of the pandemic response, adding that concerns about the economic impact should not lead Wisconsinites to disavow public health guidance.

“I’m not going to gather in crowds,” said Mr. Johnson, who said he is donning a mask when he goes grocery shopping near his home in Oshkosh. “I have enough fear and respect of this illness that I’m not going to do that myself. I’m not encouraging anybody to do it.”

Still, few people wore masks or other protective equipment at the weekend rallies. And Mr. Vos, who wore body-length personal protective equipment during his shift as a poll monitor in his hometown, Burlington, on April 7, declined to say in an interview whether it is safe for thousands of people to gather in protest at the State Capitol.

“I’m not a doctor,” Mr. Vos said. “I don’t give advice to people on how surgery should be done. I think people should make their own choices.”

Lisa Lerer and Lauren Justice contributed reporting