Republicans in Wisconsin are engaged in an all-out assault on the state’s election infrastructure, building off their attempts to challenge the results of the 2020 presidential race by pressing to give themselves full control over voting in the state.

The Republican effort — broader and more forceful than that in any other state where allies of former President Donald J. Trump are trying to overhaul elections — takes direct aim at the bipartisan Wisconsin Elections Commission, an agency Republicans created half a decade ago that has been under attack since the chaotic aftermath of last year’s election.

The firestorm picked up late last month after a long-awaited report on the 2020 results that was ordered by Republican state legislators found no evidence of fraud but made dozens of suggestions for the election commission and the G.O.P.-led Legislature, turbocharging Republican demands for more control of elections.

Then the Trump-aligned sheriff of Racine County, the state’s fifth most populous county, recommended felony charges against five of the six members of the election commission for guidance they had given to municipal clerks early in the pandemic. The Republican majority leader of the State Senate later seemed to give a green light to that proposal, saying that “prosecutors around the state” should determine whether to bring charges.

And last week, Senator Ron Johnson, a Republican, said that G.O.P. state lawmakers should unilaterally assert control of federal elections, claiming that they had the authority to do so even if Gov. Tony Evers, a Democrat, stood in their way — an extraordinary legal argument debunked by a 1932 Supreme Court decision and a 1964 ruling from the Wisconsin Supreme Court. His suggestion was nonetheless echoed by Michael Gableman, a conservative former State Supreme Court justice who is conducting the Legislature’s election inquiry.

Republican control of Wisconsin elections is necessary, Mr. Johnson said in an interview on Wednesday, because he believes Democrats cheat.

“Do I expect Democrats to follow the rules?” said the senator, who over the past year has promoted fringe theories on topics like the Capitol riot and Covid vaccines. “Unfortunately, I probably don’t expect them to follow the rules. And other people don’t either, and that’s the problem.”

The uproar over election administration in Wisconsin — where the last two presidential contests have been decided by fewer than 23,000 votes each — is heightened by the state’s deep divisions and its pivotal place in American politics.

Some top Republican officials in Wisconsin privately acknowledge that their colleagues are playing to the party’s base by calling for state election officials to be charged with felonies or for their authority to be usurped by lawmakers.

Adding to the uncertainty, Mr. Johnson’s proposal has not yet been written into legislation in Madison. Mr. Evers has vowed to stop it.

“The outrageous statements and ideas Wisconsin Republicans have embraced aren’t about making our elections stronger, they’re about making it more difficult for people to participate in the democratic process,” Mr. Evers said Thursday. The G.O.P.’s election proposals, he added, “are nothing more than a partisan power grab.”

Yet there is no guarantee that the Republican push will fall short legally or politically. The party’s lawmakers in other states have made similar moves to gain more control over election apparatus. And since the G.O.P. won control of the Wisconsin Legislature in 2010, the state has served as an incubator for conservative ideas exported to other places.

“In Wisconsin we’re heading toward a showdown over the meaning of the clause that says state legislatures should set the time, manner and place of elections,” said Kevin J. Kennedy, who spent 34 years as Wisconsin’s chief election officer before Republicans eliminated his agency and replaced it with the elections commission in 2016. “If not in Wisconsin, in some other state they’re going to push this and try to get a U.S. Supreme Court ruling on this.”

Next year, Wisconsin will host critical elections for Mr. Johnson’s Senate seat and for statewide offices, including the governor. Rebecca Kleefisch, the leading Republican in the race to challenge Mr. Evers, is running on a platform of eliminating the state election commission. (On Monday, she filed a lawsuit against the agency asking the Wisconsin Supreme Court to declare that the commission’s guidance violates state law.)

The Republican anger at the Wisconsin Elections Commission, a body of three Democrats and three Republicans that G.O.P. lawmakers created in part to eliminate the investigatory powers of its predecessor agency, comes nearly 20 months after commissioners issued guidance to local election clerks on how to deal with the coronavirus pandemic.

Republicans have seized in particular on a March 2020 commission vote lifting a rule that required special voting deputies — trained and dispatched by municipal clerks’ offices — to visit nursing homes twice before issuing absentee ballots to residents. The special voting deputies, like most other visitors, were barred from entering nursing homes early in the pandemic, and the commission reasoned that there was not enough time before the April primary election to require them to be turned away before mailing absentee ballots.

The vote was relatively uncontroversial at the time: No lawsuits from Republicans or anyone else challenged the guidance. The procedure remained in place for the general election in November.

But after Joseph R. Biden Jr. won Wisconsin by 20,682 votes out of 3.3 million cast, Republicans began making evidence-free claims of fraudulent votes cast from nursing homes across the state. Sheriff Christopher Schmaling of Racine County said the five state election commissioners who had voted to allow clerks to mail absentee ballots to nursing homes without the visit by special voting deputies — as is prescribed by state law — should face felony charges for election fraud and misconduct in office.

Robin Vos, the Republican speaker of the State Assembly, who represents Racine County, quickly concurred, saying that the five commissioners — including his own appointee to the panel — should “probably” face felony charges.

The commissioners have insisted they broke no laws.

Ann Jacobs, a Democrat who is the commission’s chairwoman, said she had no regrets about making voting easier during the pandemic and added that “even my Republican colleagues” were afraid about the future of fair elections in the state.

“We did everything we could during the pandemic to help people vote,” she said.

Mr. Johnson — a two-term senator who said he would announce a decision on whether to seek re-election “in the next few weeks” — is lobbying Republican state legislators, with whom he met last week at the State Capitol, to take over federal elections.

“The State Legislature has to reassert its constitutional role, assert its constitutional responsibility, to set the times, place and manner of the election, not continue to outsource it through the Wisconsin Elections Commission,” Mr. Johnson said. “The Constitution never mentions a governor.”

Mr. Johnson acknowledged that his proposal could leave the state with dueling sets of election regulations, one from the Wisconsin Elections Commission and another from the Legislature.

“I suppose some counties will handle it one way and other counties will handle it another,” he said.

Even if Republican lawmakers adopted Mr. Johnson’s proposal, it would apply only to federal elections, not those for state office.

Mr. Vos told reporters in Madison he had not studied whether Wisconsin legislators could take control of federal elections without the governor’s input. Devin LeMahieu, a Republican who is the State Senate majority leader, has expressed doubts about Mr. Johnson’s legal theory.

The state’s grass-roots conservatives remain angry about Mr. Biden’s victory and the failure of Republicans to undertake an Arizona-style review of ballots cast in Wisconsin last year. At least 10 Republican state lawmakers have called for the resignation of Meagan Wolfe, the commission’s nonpartisan administrator, or of the election commissioners, according to The Milwaukee Journal Sentinel.

If Ms. Wolfe were to resign, her replacement would require a majority vote of the evenly split commission. If it could not reach agreement in 45 days, the State Senate, controlled by Republicans, would choose.

“The current director of W.E.C. needs to step down,” State Senator Duey Stroebel, a Republican who sits on his chamber’s elections committee, said in an interview. “Maybe we give it another try with the W.E.C., but this administrator has proved to be incompetent and not always willing to follow the law.”

Ms. Wolfe said on Thursday that Republicans’ goal was “to pressure nonpartisan election administrators like me into resigning or vacating the election space so we can be replaced by political actors who can be convinced to carry out a partisan mission.”

At the same time, some Wisconsin Republicans continue to challenge the 2020 outcome.

On Wednesday, Timothy S. Ramthun, a Republican member of the State Assembly, formally proposed decertifying Wisconsin’s election results, reclaiming the state’s “10 fraudulent electoral ballots” cast for Mr. Biden and conducting “a full forensic physical and cyber audit” of the election.

Anticipating Mr. Ramthun’s proposal, the Legislature’s lawyers issued a report on Nov. 1 stating that there was “no mechanism” under the law to reverse a certified election.

“I invite you to see it from the eyes of the people,” Mr. Ramthun wrote to fellow legislators, urging them to correct “the most egregious injustice we have seen in our time.”

The next day, Mr. Trump publicly congratulated Mr. Ramthun.

Wisconsin Democrats, exasperated and locked out of power in the Legislature, have been left to issue increasingly dire warnings.

“If this was some kind of Hollywood farce or a madcap political comedy, you would say that’s not credible even for a fake show,” said Kelda Roys, a Democratic state senator. “There’s real consequences to this. It’s designed to take away the guardrails to our democracy that keep us fair and free.”

Kitty Bennett contributed research.