Outside money has poured into New Hampshire heading into Tuesday’s primary as Republicans eye three opportunities to pick up Democratic-held seats, above all that of Senator Maggie Hassan, one of her party’s most vulnerable incumbents.But the leading G.O.P. candidate for Senate, Don Bolduc, is an election denier with a history of outlandish statements. His closest rival, Chuck Morse, the State Senate president, is playing on fears that nominating Mr. Bolduc could mean squandering a major opening.Ms. Hassan, a Democrat, narrowly won the seat in 2016. In a 50-50 U.S. Senate, every competitive race has the potential to tip the balance of power.New Hampshire, Rhode Island and Delaware are all holding primaries on Tuesday. It’s not a big night, but it’s the last round of voting before the November midterm elections.Here are the races to watch.Don Bolduc, a retired Army general, center, during a campaign appearance at the American Legion in Laconia, N.H., on Saturday.John Tully for The New York TimesA competitive Senate primaryPresident Biden carried New Hampshire by seven percentage points in 2020, and successful statewide Republican politicians have tended to hew to the center, appealing to independents and conservative Democrats. But Mr. Bolduc, a retired Army general, has not only embraced Mr. Trump’s lie that he won the 2020 presidential election, he has also called Gov. Chris Sununu a “Chinese Communist sympathizer” and questioned whether the United States still needs the F.B.I. (Mr. Sununu has called Mr. Bolduc a conspiracy theorist.) Money from super PACs with ties to both Republican and Democratic Senate leadership has flowed in to try to tip the scales, with the Senate Majority PAC, a Democratic group, spending millions to attack Mr. Morse, the establishment-backed candidate — a gambit that could aid Mr. Bolduc. Mr. Morse, who has the backing of Mr. Sununu and establishment Republicans but is trailing Mr. Bolduc by double digits in polls, met with Mr. Trump at the former president’s New Jersey golf club on Sept. 2, but no endorsement has materialized.Then again, Mr. Trump hasn’t endorsed Mr. Bolduc, either.A scramble for House seats Republicans in New Hampshire are wrangling over the chance to square off against U.S. Representatives Chris Pappas and Ann McLane Kuster, two Democrats whom Republicans see as vulnerable. Matt Mowers, who worked in the State Department during the Trump administration, and Karoline Leavitt, who worked in the White House communications office, are the leading candidates in a 10-person field in Mr. Pappas’s First District, which zigzags across much of eastern and southern New Hampshire..css-1v2n82w{max-width:600px;width:calc(100% – 40px);margin-top:20px;margin-bottom:25px;height:auto;margin-left:auto;margin-right:auto;font-family:nyt-franklin;color:var(–color-content-secondary,#363636);}@media only screen and (max-width:480px){.css-1v2n82w{margin-left:20px;margin-right:20px;}}@media only screen and (min-width:1024px){.css-1v2n82w{width:600px;}}.css-161d8zr{width:40px;margin-bottom:18px;text-align:left;margin-left:0;color:var(–color-content-primary,#121212);border:1px solid var(–color-content-primary,#121212);}@media only screen and (max-width:480px){.css-161d8zr{width:30px;margin-bottom:15px;}}.css-tjtq43{line-height:25px;}@media only screen and (max-width:480px){.css-tjtq43{line-height:24px;}}.css-x1k33h{font-family:nyt-cheltenham;font-size:19px;font-weight:700;line-height:25px;}.css-ok2gjs{font-size:17px;font-weight:300;line-height:25px;}.css-ok2gjs a{font-weight:500;color:var(–color-content-secondary,#363636);}.css-1c013uz{margin-top:18px;margin-bottom:22px;}@media only screen and (max-width:480px){.css-1c013uz{font-size:14px;margin-top:15px;margin-bottom:20px;}}.css-1c013uz a{color:var(–color-signal-editorial,#326891);-webkit-text-decoration:underline;text-decoration:underline;font-weight:500;font-size:16px;}@media only screen and (max-width:480px){.css-1c013uz a{font-size:13px;}}.css-1c013uz a:hover{-webkit-text-decoration:none;text-decoration:none;}How Times reporters cover politics. We rely on our journalists to be independent observers. So while Times staff members may vote, they are not allowed to endorse or campaign for candidates or political causes. This includes participating in marches or rallies in support of a movement or giving money to, or raising money for, any political candidate or election cause.Learn more about our process.Mr. Mowers, who lost to Mr. Pappas in 2020, earned the endorsements of the House minority leader, Kevin McCarthy, and the minority whip, Steve Scalise. Representative Elise Stefanik of New York, the third-ranking House Republican, is supporting Ms. Leavitt, who once worked for her. 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.Odds and endsThat’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.In Rhode Island, Gov. Daniel McKee, the state’s former lieutenant governor, is seeking his first full term after replacing former Gov. Gina Raimondo, who left to serve in the Biden administration as commerce secretary. He faces four challengers in the Democratic primary, including Nellie Gorbea, the Rhode Island secretary of state.Republican hopes of recapturing the governor’s office rest on Ashley Kalus, a first-time candidate who moved to Rhode Island in 2021, and Jonathan Riccitelli, the owner of a hotel and building maintenance company, whose criminal record — much of it under another name — was reported by The Boston Globe. A college freshman, Zachary Hurwitz, also collected enough signatures to run as an independent.In Delaware, which has neither a Senate nor a governor’s race this year, the biggest contest is for state auditor, after the incumbent Democrat, Kathleen K. McGuiness, was convicted of official misconduct, conflict of interest and structuring a contract to avoid a procurement policy, all misdemeanors. In response, the state Democratic Party threw its support behind a challenger, Lydia York, a lawyer and accountant. More