What to Watch in Tuesday’s Primary Elections

The marquee races on Tuesday are taking place in South Carolina, where two Republican House members are facing Trump-backed challengers, and in Nevada, where Republicans are aiming to sweep a host of Democratic-held seats in the November general election.

Voters in Maine and North Dakota will also go to the polls, and in Texas, Republicans hope to grab the Rio Grande Valley seat of Representative Filemon Vela, a Democrat who resigned in March.

The primary season has had more extensive Election Days, but Tuesday has plenty of drama. Here is what to watch.

In South Carolina, a showdown with Trump

Representatives Tom Rice and Nancy Mace crossed former President Donald J. Trump in the opening days of 2021 as the cleanup crews were still clearing debris from the Jan. 6 assault on the Capitol. Mr. Rice was perhaps the biggest surprise vote in favor of impeachment — as a conservative in a very conservative district, he was risking his political career.

Ms. Mace voted against impeachment, but in her first speech in Congress that January, she said the House needed to “hold the president accountable” for the Capitol attack.

So Mr. Trump backed two primary challengers: State Representative Russell Fry against Mr. Rice, and the conservative Katie Arrington against Ms. Mace.

In Ms. Mace’s case, the Trump world is divided. Mr. Trump’s first United Nations ambassador, Nikki Haley, and one of his chiefs of staff, Mick Mulvaney, both South Carolinians, are backing the incumbent freshman.

That is, in part, because Ms. Arrington has a poor track record: In 2018, after beating then-Representative Mark Sanford in the Republican primary after he castigated Mr. Trump, she then lost in November to a Democrat, Joe Cunningham. (Mr. Cunningham, who was defeated by Ms. Mace in 2020, is hoping for a comeback this year with a long-shot bid to defeat the incumbent governor, Henry McMaster.)

Republicans worry that an Arrington victory on Tuesday could jeopardize the seat, which stretches from Charleston down the affluent South Carolina coast.

Mr. Rice’s path to victory on Tuesday will be considerably harder, but he remains defiant about his impeachment vote. “Defending the Constitution is a bedrock of the Republican platform. Defend the Constitution, and that’s what I did. That was the conservative vote,” he said in a June 5 interview on ABC’s “This Week,” adding, “There’s no question in my mind.”

Battleground Nevada

California may have a larger number of seats in play, but no state is as thoroughly up for grabs as Nevada. Three out of four of the state’s House seats are rated tossups — all three of which are now held by Democrats. Other tossup races include the Senate seat held by Catherine Cortez Masto, a Democrat, and the governorship held by Steve Sisolak, also a Democrat. A Republican sweep would do real damage, not only to the Democrats’ narrow hold on Congress, but also to their chances in the 2024 presidential election if Nevada is close: It’s better to have the governor of a state on your side than on the other side.

But first, Republican voters need to sort through a vast array of candidates vying for each position. Joe Lombardo, the sheriff of Las Vegas’s Clark County, is the favorite for the Republican nomination to challenge Mr. Sisolak. He has Mr. Trump’s endorsement and echoes Mr. Trump’s language in his pledge to “take our state back.”

Eight candidates are vying to challenge Ms. Cortez Masto, but Adam Laxalt, the former Nevada attorney general who lost to Mr. Sisolak in 2018, is clearly favored.

Representative Dina Titus, a Democrat, also has eight Republicans competing to challenge her, including a former House member, Cresent Hardy. But it’s Carolina Serrano, a Colombian American immigrant, who has the backing of Republican leaders and the Trump world alike, with endorsements from Representative Elise Stefanik of New York, the party’s No. 3 House leader, as well as Mr. Laxalt and Richard Grenell, a pugilistic former national security official in the Trump administration.

Five Republicans hope to challenge Representative Susie Lee, a Democrat. Among them, April Becker, a real estate lawyer, has raised the most money by far and has the backing of the House Republican leader, Kevin McCarthy, as well as Ms. Stefanik, Ms. Haley and Mr. Laxalt.

The potential G.O.P. challengers to Representative Steven Horsford, a Democrat, are most clearly divided between the Trump fringe and the party’s mainstream. Sam Peters, an insurance agent, is backed by the far-right Arizona congressmen Paul Gosar and Andy Biggs, who both have been tied to extremist groups, as well as the right-wing rocker Ted Nugent. Annie Black, an assemblywoman running in the primary against Mr. Peters, is more mainstream.

A harbinger brewing in South Texas

When Mr. Vela decided to resign from the House instead of serving out the rest of his term, he most likely did not know the stakes he was creating for the special election to fill his seat for the remaining months of this year.

Republicans are trying to make a statement, pouring money into the traditionally Democratic Rio Grande Valley district to support Mayra Flores. She has raised 16 times the amount logged by her closest Democratic competitor, Dan Sanchez.

A Flores victory would be proclaimed by Republicans as a sign of worse to come for Democrats in November.

The district, Texas’s 34th, has been redrawn for the general election to be overwhelmingly Democratic. But Republicans are hoping the battleground will shift just westward, to the 15th district, which was drawn to be dead even.

Republicans are backing Monica de la Cruz for that race. If Tuesday’s special election goes their way, they may also invest heavily in the next seat to the west as well, the 28th District, where Representative Henry Cuellar, a long-serving moderate Democrat, appears to be narrowly holding a lead over his progressive challenger, Jessica Cisneros, who is seeking a recount in the razor-thin runoff.

A rivalry over Medicaid in Maine

The Northeastern tip of the nation wasn’t known for bare-knuckled politics before Paul LePage, a Trump-like Republican who predated Mr. Trump, won the governorship in 2010. In successive elections, Mr. LePage was helped by the state’s tradition of producing and voting for independent candidates, who siphoned enough votes from whomever his Democratic challenger was to let him win with a plurality.

He retired from the governor’s office in 2018 and was succeeded by a Democrat, Gov. Janet Mills, who set out to expand Medicaid under the Affordable Care Act.

Mr. LePage had vetoed the expansion six times before it was passed by a voter referendum in 2017. Even then, he ignored the will of the voters and refused to implement the expansion. Out of office, he said he would decide whether to challenge Ms. Mills depending on if she expanded Medicaid in what he called a cost-effective way.

Now he is seeking a comeback, and he has no primary opponent to stop him.

In the north of the state is one of the country’s most endangered House Democrats, Jared Golden, who has repeatedly defied Democratic leadership to demonstrate his bona fides as a centrist. He was the only House Democrat who voted against President Biden’s far-reaching social safety net and climate change bill, Build Back Better, and he voted with Republicans last week against a suite of Democratic gun control measures.

Republicans think they can beat Mr. Golden anyway. Bruce Poliquin, a former House member whom Mr. Golden defeated in 2018 by 3,509 votes, has raised a lot of money and now has more cash on hand than Mr. Golden. But Mr. Poliquin first needs to get by a primary challenger, Elizabeth Caruso, a local official in tiny Caratunk, Me.