Five Takeaways From Tuesday’s Elections

The day after F.B.I. agents searched his home in Mar-a-Lago, former President Donald J. Trump yet again illustrated his electoral pull on the Republican Party.

In a series of primaries in Wisconsin, Minnesota, Vermont and Connecticut on Tuesday — and in a newly conceded race from last week’s election in Washington State — Mr. Trump’s candidates scored victories and his enemies drew defeats, with a notable exception.

Republican voters in Wisconsin and Minnesota elevated a slate of nominees who have peddled baseless claims of fraud over the 2020 presidential election, setting up high-stakes battles in the fall over the future of fair elections in critical battleground states. And in Connecticut, the Trump-backed Senate candidate Leora Levy trounced a moderate Republican, Themis Klarides.

Here are five takeaways.

One of the country’s pivotal races for governor takes shape.

Tony Evers, Wisconsin’s Democratic governor, was always going to be in trouble.

He was facing a prospective showdown against either Tim Michels, a millionaire construction magnate endorsed by Mr. Trump, or Rebecca Kleefisch, the state’s lieutenant governor who had the backing of former Vice President Mike Pence. On Tuesday night, Mr. Evers learned his Republican rival would be Mr. Michels, the latest victor of the power struggle across the country between Trump Republicans and establishment Republicans.

Mr. Michels might not be the best onstage, but he has money to pour into his race. And he could go after not only Mr. Evers but Wisconsin Republicans’ other favorite target, President Biden. It was Mr. Biden who canceled the contract to build the Keystone XL pipeline, which Mr. Michel’s firm was supposed to build.

The electoral contest is likely to be one of the most consequential in the country.

Mr. Evers, who has cast himself as a defender of fair elections, has vetoed more than a dozen state bills that would have restricted voting. Mr. Michels has pushed the false notion that the 2020 election can still be decertified and has pledged to abolish the state’s elections commission.

Mr. Michels has campaigned on being tough on crime. On Tuesday, that stance did not apply to the former president. He called the search of Mr. Trump’s Florida home an “overzealous prosecution” and dismissed the possibility that Mr. Trump could have committed a crime.

Trump fever has not quite broken.

Robin Vos, the speaker of the Wisconsin Assembly, came within a whisker of losing on Tuesday to a candidate with little name recognition, all thanks to a Trump endorsement. The near miss for Mr. Vos, the most powerful Republican in Wisconsin politics, shows just how crucial that endorsement can be in the land of cheese and election rejection.

The race between Mr. Vos and Adam Steen in the Republican primary for a Wisconsin Assembly seat was tighter than virtually any Wisconsin analysts predicted, though Mr. Vos is an 18-year incumbent who has been speaker for a decade and who grew up in the district. Mr. Steen is an Indiana native who had no paid advertising beyond a small bit of mailings, but he had Mr. Trump’s backing and a claim that he would work to take back the state’s 10 Electoral College votes from 2020, a legal impossibility.

Mr. Steen’s far-right views extended well beyond election denialism. In an interview, he also said he would seek to make contraception illegal in Wisconsin.

A ray of hope for Democrats.

In a state where the last two presidential elections were won by razor-thin margins, Democrats in Wisconsin have some cause for optimism.

Some of that has to do with sweeping legislation, covering climate change and prescription drug prices, which is on pace to pass by November. Some of it has to do with the energy galvanizing Democratic voters over abortion rights. And some of it, in Wisconsin, has to do with Mandela Barnes, the state’s lieutenant governor.

Mr. Barnes — a former community organizer from Milwaukee — won the Democratic nomination in a Senate race to take on the Republican incumbent, Senator Ron Johnson. Mr. Barnes’s victory sets up a heated general election race that could help decide control of the Senate. Mr. Barnes, Wisconsin’s first Black lieutenant governor, would be its first Black senator if he were to win.

One test for Mr. Barnes will be whether he can increase his fund-raising levels. He is entering the general election with nearly $1 million cash on hand, according to the latest federal election filings. For Mr. Johnson, that number was more than $2 million.

Another Republican impeacher will not return to Congress.

Of the 10 House Republicans who voted to impeach Mr. Trump, the fate of all but one is now sealed. Four declined to seek another term, two others survived their primaries and three have lost.

In Washington State, Representative Jaime Herrera Beutler, who sharply criticized Mr. Trump’s actions leading up to the Jan. 6, 2021, attack on the Capitol, became the third House Republican to lose, after she conceded her race with a statement on Tuesday. “I’m proud that I always told the truth, stuck to my principles, and did what I knew to be best for our country,” she said.

The 10th House Republican who voted to impeach the former president, Representative Liz Cheney of Wyoming, has her primary next week on Aug. 16. She has long stopped seeing the election as a test of political survival, and is instead using it as a way to make her case against Mr. Trump and restore a party that she sees as “very sick.”

The ‘squad’ remains intact.

Representative Ilhan Omar, one of the most prominent lawmakers in Congress, survived her Democratic primary in Minnesota as she seeks a third term, making her the latest member of the progressive group known as the “squad” to defend her seat this year.

Don Samuels, a former Minneapolis city councilman and school board member, lost by two percentage points in a hard-fought race in Minnesota’s Fifth Congressional District. Mr. Samuels ran as a centrist who challenged her on policing issues. He had the support of some of the Democratic establishment and Mayor Jacob Frey of Minneapolis.

Ms. Omar’s victory against Mr. Samuels makes her the third member of the “squad” to beat back primary challengers. The other two were Representatives Cori Bush of Missouri and Rashida Tlaib of Michigan.

Two other members — Representatives Alexandria Ocasio-Cortez of New York and Ayanna Pressley of Massachusetts — did not draw any primary opponents this cycle. A sixth member, Representative Jamaal Bowman of New York, is facing three primary challengers later this month.