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 TrumpRepresentatives 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.Representative Tom Rice speaking with supporters in Conway, S.C., last week.Madeline Gray for The New York TimesIn 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 NevadaCalifornia 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.Adam Laxalt, a Republican Senate candidate, with supporters in Moapa Valley, Nev., last week.Joe Buglewicz for The New York TimesRepresentative 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 TexasWhen 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 campaign sign for Mayra Flores in Brownsville during the Texas primary in March.Denise Cathey/The Brownsville Herald, via Associated PressA Flores victory would be proclaimed by Republicans as a sign of worse to come for Democrats in November.Understand the 2022 Midterm ElectionsCard 1 of 6Why are these midterms so important? More