Mr. Mowers, who lost to Mr. Pappas in 2020, earned the endorsements of House Minority Leader Kevin McCarthy and Minority Whip Steve Scalise. Representative Elise Stefanik of New York, the third-ranking House Republican, is supporting Ms. Leavitt, who once worked for her.

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Ms. Leavitt and other Republican contenders have portrayed Mr. Mowers as an establishment tool and criticized him for voting in 2016 in both the New Jersey and New Hampshire primaries. (He voted in New Jersey before moving to New Hampshire to work on Chris Christie’s presidential campaign.) Mr. Mowers has defended himself by channeling Mr. Trump, saying he was being attacked because he had planned to “shake up the status quo.”

In New Hampshire’s Second District, encompassing the rest of the state, seven Republicans are competing to face Ms. Kuster, a longtime adoption lawyer who is seeking her sixth term.

George Hansel, the two-term Republican mayor of the liberal town of Keene, has the endorsement of Mr. Sununu. Other contenders include Bob Burns, the former Hillsborough county treasurer, and Lily Tang Williams, who ran for the Senate in Colorado as a Libertarian in 2016.

In Rhode Island, six contenders are vying in the Democratic primary for the seat held by Representative Jim Langevin, who is retiring after 11 terms. Seth Magaziner, the state’s general treasurer, held a sizable lead in early polling. On the Republican side, Allan Fung, the former mayor of Cranston, is running uncontested.

That’s about it for what constitutes the excitement in Tuesday’s voting.

In the New Hampshire governor’s race, Mr. Sununu, who declined to run for the Senate, is considered virtually untouchable in his drive for a fourth term. He faces negligible opposition in his primary and is heavily favored in November against Tom Sherman, a state senator who is uncontested in the Democratic primary for governor.