G.O.P. Impeachment Threats : Republicans in Wisconsin are coalescing around the prospect of impeaching a newly seated liberal justice on the state’s Supreme Court, whose victory in a costly, high-stakes election this spring swung the court in Democrats’ favor and threatened the G.O.P.’s iron grip on state politics.

The push, just five weeks after Justice Janet Protasiewicz joined the court and before she has heard a single case, serves as a last-ditch effort to stop the new 4-to-3 liberal majority from throwing out Republican-drawn state legislative maps and legalizing abortion in Wisconsin.

The drama over Republican threats to impeach and possibly remove Justice Protasiewicz could raise new questions about democracy and the legitimacy of elections in a state where G.O.P. lawmakers and their allies spent two years disputing the 2020 presidential contest’s outcome.

G.O.P. Impeachment Threats : For Republicans, the liberal Supreme Court majority serves as an existential danger. If the court, as expected, invalidates Wisconsin’s legislative maps, it would strip Republicans of what now amounts to permanent majorities in the Legislature. But removing a newly elected justice could prompt a backlash in 2024 from Democrats and moderate Republican voters who abandoned the G.O.P. during the Trump years.

After weeks of watching Republicans openly ponder impeachment, Democrats on Wednesday will begin a $4 million counteroffensive over three weeks that is intended to inflict maximum political pain on legislators who vote to block Justice Protasiewicz from serving.

At issue for Wisconsin Republicans are Justice Protasiewicz’s stated views on Wisconsin’s legislative maps. In a deliberate strategy to energize and win support from Democratic donors and voters during her campaign this spring, she was unusually blunt about her positions on issues including abortion rights and the state’s maps, which she called “rigged.”

The day after she was seated last month, liberal groups filed a legal challenge to the maps. Republicans immediately demanded that she recuse herself from the case — which would almost certainly cause a 3-to-3 deadlock on the State Supreme Court.

Former Gov. Scott Walker, who remains popular among Wisconsin Republicans, said the Assembly was “obligated” to impeach Justice Protasiewicz if she tried to rule on the maps.

“If she does not remove herself from the case, the members of the State Assembly should vote to impeach Justice Protasiewicz,” Mr. Walker said.

Justice Protasiewicz has said nothing publicly about the case. She declined to comment, but on Tuesday she released a letter she had received from the Wisconsin Judicial Commission, an independent body that investigates complaints against judges, dismissing complaints that she had violated the state’s judicial code of ethics by stating her “personal views” about abortion and Wisconsin’s legislative maps.

The Republican Party beyond Wisconsin is seeking to use impeachment as a first line of defense against Democratic officials.

In Georgia, Republican legislators have been agitating for a special session to impeach Fani T. Willis, the Democratic prosecutor who brought a wide-ranging indictment against former President Donald J. Trump and others who sought to overturn the 2020 election results. And in Washington, some House Republicans are pushing to impeach President Biden.

In Wisconsin, leading Republicans have not been subtle about their intentions.

Robin Vos, the powerful Assembly speaker, has twice in recent weeks raised the possibility of impeachment. He told The Associated Press last week that “we have to take a look at it.” Mr. Vos did not respond to messages on Tuesday.

Senator Ron Johnson, who before the midterm elections called for the State Legislature to seize control of federal elections in the state, said legislators should impeach Justice Protasiewicz before she could hear a case on the maps.

“She obviously should recuse herself from any redistricting case, and if she doesn’t, the Legislature has the ability” to impeach her, he said in a text message. “I hope they would.”

Republicans would control all levers of the impeachment process. They hold a 29-seat majority in the State Assembly, where a majority is required to impeach state officials, and a two-thirds majority in the State Senate, the precise number of votes needed to convict and remove someone impeached by the Assembly.

Upon impeachment, a Supreme Court justice would be prohibited under the State Constitution from participating in and voting on court decisions. If the State Senate voted to convict and remove Justice Protasiewicz before Dec. 1, Gov. Tony Evers, a Democrat, would name a replacement who would face voters next April — when the Republican presidential primary will be on the ballot, meaning that conservative voters would be highly energized.

There is little precedent to determine how an impeachment would play out. The Wisconsin Constitution stipulates that impeachment is intended for “corrupt conduct in office or for the commission of a crime or misdemeanor.”

No Wisconsin judge has been impeached since 1853, when legislators removed a Milwaukee circuit court judge in a bribery scandal, according to Robert Yablon, a co-director of the State Democracy Research Initiative at the University of Wisconsin Law School.

As at the U.S. Supreme Court, recusal decisions are left to the Wisconsin justices themselves. In years past, conservative justices have argued that personal views they had previously stated did not mean they were required to recuse themselves from relevant cases.

For example, Justice Brian Hagedorn once compared homosexuality to bestiality, called Planned Parenthood “a wicked organization” and wrote that “Christianity is the correct religion, and that insofar as others contradict it, they are wrong.” He has said those statements would not warrant his recusal on cases about abortion, gay rights or religion.

So far, Republicans appear remarkably unified around the idea of impeaching Justice Protasiewicz. No G.O.P. member of the Legislature has spoken out against it, despite private concerns among some in the party that seeking to remove a newly elected justice would be politically catastrophic.

“It’s absurd,” said Paul Bucher, a Republican who spent 22 years as the Waukesha County district attorney. “This jump to impeachment, that’s just what we do today to people we don’t like in office.”

Wisconsin Democrats are aghast at what they view as another attempt by Republicans to reject the outcome of an election they lost. Many now privately concede that impeaching Justice Protasiewicz is a foregone conclusion.

“They’re deliberately trying to overturn the will of the people,” said Sarah Godlewski, the Democratic secretary of state. “We have to understand the risk this is posing. It’s a potential reality that would put Wisconsin’s democracy in jeopardy.”

The Democratic Party of Wisconsin on Wednesday and its allies are set to begin what its chairman, Ben Wikler, described as a voter mobilization project on par with its statewide get-out-the-vote operations.

The coalition will be advertising on television, the internet and through the mail while mobilizing the party’s volunteer base to knock on doors in Republican districts to warn legislators against impeaching Justice Protasiewicz.

“The longer they push this forward, the more political price we want to build for Republicans in the Legislature and the whole G.O.P. machinery,” Mr. Wikler said. “This could become a fireball that eats all of them up throughout 2024.”

National Democrats, who poured millions of dollars into Justice Protasiewicz’s election, have begun to sound alarms in Washington.

“Impeaching Justice Protasiewicz is as absurd as it is dangerous,” said Eric H. Holder Jr., the former attorney general, who is now the chairman of the National Democratic Redistricting Committee. “America is supposed to be a democracy where the will of the people stands, even if some power-hungry politicians disagree.”

In April, Justice Protasiewicz won a commanding victory in what was widely seen as a referendum on abortion rights. Her 11-point margin was a blowout in Wisconsin, a purple state where presidential contests are routinely decided by fewer than 25,000 votes. She carried 12 Republican-held districts in the State Assembly and six in the State Senate.

But there is little evidence that even Republicans in those districts are hesitant about removing her from office. One of them, State Senator Dan Knodl, who won a special election on the same April ballot that elected Justice Protasiewicz, floated impeachment even before Election Day.

On Tuesday, The New York Times contacted all 18 of the Republican legislators in districts Justice Protasiewicz won. Only one, John Macco, an Assembly member from Green Bay, agreed to be interviewed.

Mr. Macco said it was “outrageous” that Justice Protasiewicz would agree to hear the redistricting case after stating her views about the legislative maps, but he declined to say whether he would vote for impeachment. He said the Assembly had not yet discussed it, adding that it had a “fiduciary responsibility” to serve as a check against rulings by Justice Protasiewicz that it believes are unfair.

“I got elected five times here in this district,” Mr. Macco said. “This district went for Trump, this district went for Walker. I can’t tell you why they went for that justice. Do we not, all of us conservatives who got elected, also have a responsibility to act?”