Two states are holding primary elections on Tuesday. In one, Joe Biden couldn’t crack 40 percent of the vote in 2020; in the other, he couldn’t even get to 30 percent.

You guessed it: Most of the action is on the Republican side.

In West Virginia, two Republican incumbents are battling for a newly drawn congressional district. In Nebraska, the Republican primary for governor has become a dead heat among three candidates.

Across the aisle in Nebraska, Democrats are preparing to take another crack at an Omaha-based House seat — one with particular national relevance, considering it’s the one congressional district in the state that gave Joe Biden an Electoral College vote in 2020.

Here’s what we’re watching.

Trump’s endorsement battles with sitting G.O.P. governors

Because Nebraska and West Virginia are so deeply Republican, the winners of Tuesday’s Republican primaries will be heavily favored to win in the November general election. The results will probably decide whether acolytes of Donald Trump will be elected to Congress and state executive offices.

“That’s why all the attention is on the primary,” said Sam Fischer, a Republican strategist in Nebraska.

Trump notched a victory in Ohio last week when J.D. Vance surged to the top of a crowded Republican primary after being endorsed by the former president. On Tuesday, the power of a Trump endorsement will be put to the test again.

But in Nebraska and West Virginia, two of the candidates who lack support from Trump have a different asset: an endorsement from the state’s current governor.

Unlike in Ohio, where Gov. Mike DeWine declined to endorse a Senate candidate as he faced a primary challenge of his own, the Republican governors of Nebraska and West Virginia appear to have had few qualms about endorsing candidates overlooked by Trump. In fact, both leaders — Gov. Pete Ricketts of Nebraska and Gov. Jim Justice of West Virginia — have publicly criticized Trump’s endorsement decisions in their respective states.

In Nebraska, Trump backed Charles Herbster, a wealthy owner of an agriculture company. Ricketts, the departing governor, is term-limited, and has not only thrown his support behind a different candidate — Jim Pillen, a University of Nebraska regent — but also publicly disparaged Herbster.

In West Virginia, Governor Justice threw his support to Representative David McKinley in the state’s House race after Trump had endorsed Representative Alex Mooney. Justice recently said he thought Trump had made a mistake.

Which is more important in G.O.P. races: The messenger or the message?

In both West Virginia and Nebraska, the candidates endorsed by the governor have accused Trump’s picks of being outsiders.

McKinley calls his Trump-backed opponent “Maryland Mooney,” drawing attention to the congressman’s past in the Maryland Legislature and in the Maryland Republican Party. Keeping with the “M” theme, Pillen has criticized his rival as “Missouri Millionaire Charles Herbster,” citing reports that Herbster has a residence in Missouri.

But if the messenger is more important than the message, the candidates endorsed by Trump have the edge.

Scott Jennings, a Republican strategist who has worked with Mitch McConnell and George W. Bush, said that with high Republican enthusiasm this year, he expected strong turnout, meaning that some voters who would normally turn out only during a presidential race — that is, when Trump is on the ticket — are likely to vote in the midterms.

Those voters are some of Trump’s most loyal followers — and some of the most wary of any other politician, Jennings said.

“These are the new Trump Republicans who came into the party with him, and these are the people least likely to care what an establishment or incumbent politician would say,” he said.

In Nebraska, the feud between Herbster and Pillen might have an unintended consequence. While they compete to be the Trumpiest and most authentically local candidates, voters could tire of the political sniping and throw their support behind Brett Lindstrom, a state senator who is the third main contender.

“The main question is, are Nebraska primary voters going to ignore the negative attacks by Herbster and Pillen?” said Fischer, the Republican strategist in the state. “And will Lindstrom benefit from that?”

There would be precedent. In a Republican primary for Senate in Nebraska in 2012, Deb Fischer won a narrow race after a bitter battle between two other candidates. And in another G.O.P. Senate primary in Indiana in 2018, two of the state’s congressmen engaged in a prolonged feud stemming from college decades earlier. Exhausted voters went with the little-known Mike Braun, now the state’s junior senator.

How much do sexual misconduct allegations matter in Republican primaries?

While Herbster has the most prized asset in the primary — Trump’s endorsement — he also faces the most serious questions about his personal history. Two women, including a Republican state senator, have publicly accused him of groping them at a political event in 2019.

Herbster has taken an approach long embraced by Trump, denying the allegations and calling them a political hit job by his detractors.

How voters respond to the allegations could signal — at least in Nebraska — where the G.O.P. base stands in tolerating candidates accused of mistreating women.

“If you can win with these allegations in Nebraska, you can probably win anywhere,” said Mike DuHaime, a Republican strategist. But if Herbster loses, DuHaime said, Trump can point to the allegations against him as the culprit, rather than the waning power of his endorsement.

Later this year in Georgia, another Trump-endorsed candidate who has faced allegations of domestic violence, Herschel Walker, is running for Senate, though he does not face a competitive primary.

And in Missouri, where Trump has not yet made an endorsement, former Gov. Eric Greitens has alarmed some Republican insiders by persisting with his bid for Senate even after his former wife accused him of abusing her and their children, the latest in a series of scandals for Greitens.

Will Democrats’ fresh start pay off in a battleground district?

The Democratic primaries in Nebraska’s Second Congressional District have been some of the most eventful in recent House history — even if few people have noticed.

In 2018, Kara Eastman, then an underfunded candidate backed by the progressive group Justice Democrats, defeated the district’s former congressman, Brad Ashford, in the primary. Democrats, sure that Eastman was too liberal for this suburban Republican-held seat, largely ignored the district, but were surprised to see how close Eastman got to winning.

In 2020, Eastman won again in the primary — this time with support from the Democratic establishment and with a messaging makeover. She defeated Ashford’s wife, Ann Ashford, in the primary. Then Brad Ashford crossed party lines to endorse Representative Don Bacon, a Republican who won re-election.

This year, Democrats are trying again, but with a new candidate. The primary comes down to Tony Vargas, a state senator, and Alisha Shelton, a mental health practitioner who placed third in the 2020 Senate primary.

“Both Tony Vargas and Alisha Shelton have built their careers on helping hardworking Nebraska families get ahead,” said Johanna Warshaw, a spokeswoman for the Democratic Congressional Campaign Committee. “No matter who wins the Democratic primary, either candidate is well positioned to take on Don Bacon and his extremist policies in this Biden-won seat.”

What to read

• Far-right activists associated with the QAnon conspiracy theory movement are intercepting migrant children at the southern border and collecting information about their families, based on an unfounded belief that they are falling prey to sex-trafficking rings, Miriam Jordan reports.

• Our colleague Ruth Graham tells the story of Kevin Thompson, an evangelical pastor in Arkansas who parted with his church as Trump-era politics intruded on his work in disconcerting ways.

• California will hold its primary elections next month. Here are three races we’re watching.

Pulse

A poll looks at immigration views and a conspiracy theory

Late last month, my colleague Jazmine Ulloa wrote about a fixation among Republican leaders and candidates on the false claim that undocumented immigrants are voting fraudulently. Today, one of the country’s most reputable pollsters indicated just how widespread this view is among the American public.

The Associated Press-NORC poll, conducted in December, found that nearly a third of U.S. adults agreed with the following statement: “There is a group of people in this country who are trying to replace native-born Americans with immigrants who agree with their political views.” People whom the study identified as tending to “engage in conspiratorial thinking” were twice as likely to agree with the statement.

Donald Trump made similar false claims throughout his term as president, but they were repeatedly debunked. Voter fraud in general is rare.

The poll also found that 29 percent of adults were “extremely” or “very” concerned that U.S.-born Americans are “losing economic, political and cultural influence” because of the growing immigrant population.

Such worries have been elevated by the Fox News host Tucker Carlson, who has repeatedly borrowed from a racist conspiracy theory, “the great replacement,” to argue that Democrats are importing supporters.

As my colleague Nicholas Confessore explained in a three-part series that analyzed 1,150 episodes of Tucker Carlson’s show, it’s just the latest iteration of a push to stoke fears of immigration — one that seems to be again gaining steam before the midterms.

— Leah