MINDEN, Nev. — Surrounded by a half-dozen construction cranes hoisting floodlights, loudspeakers and American flags into the chilly desert twilight, Joe Lombardo stood in front of an attentive audience at a Trump rally and delivered a warm tribute.“We’re here to rally for the Republican ticket, and who’s going to help us?” Mr. Lombardo, the party’s nominee for governor of Nevada, told a crowd on the Minden, Nev., airport tarmac that outnumbered the town’s population of 3,500. “The greatest president, right? Donald J. Trump!”But the praise from Mr. Lombardo, a longtime Clark County sheriff, contrasted sharply with his tepid testimonial of Mr. Trump a week earlier.Seated in a Las Vegas television studio with his hands pressed tightly together in his lap, Mr. Lombardo demurred when asked during his only scheduled debate with Gov. Steve Sisolak, the Democratic incumbent, if Mr. Trump had been a great president.“I wouldn’t use that adjective — I wouldn’t say great,” Mr. Lombardo answered. “He was a sound president.”Heading into the final weeks of the midterm campaigns, Republican candidates locked in close races, as Mr. Lombardo is, have twisted themselves into political contortions as they puzzle out how to handle their party’s most powerful figure — and its most controversial — while toggling between the debate stage and the rally stage.At a rally last week in Nevada, Joe Lombardo referred to Donald J. Trump as “the greatest president.” But during a debate, when asked, he said “he was a sound president.”Bridget Bennett for The New York TimesThe challenge confronting Republican contenders across the country is how to win over moderate and independent swing voters without alienating the party’s base of Trump loyalists — or the former president himself. Mr. Trump often views politics in deeply personal terms and is known to respond in kind to acts of defiance, even when retribution could jeopardize an election for his party.Democrats are similarly trapped in an awkward dance with President Biden, whose low approval ratings have forced candidates to keep him at an arm’s distance. But polls show that Mr. Biden’s political brand is not as polarizing as Mr. Trump’s. To like Mr. Trump is to love him, while disapproval is often on par with disdain.In a New York Times/Siena College poll last month, more than half of the voters who said they viewed Mr. Trump favorably said they viewed him very favorably, while four out of five who had unfavorable opinions of the former president said they viewed him very unfavorably.The State of the 2022 Midterm ElectionsWith the primaries over, both parties are shifting their focus to the general election on Nov. 8.The Final Stretch: With less than one month until Election Day, Republicans remain favored to take over the House, but momentum in the pitched battle for the Senate has seesawed back and forth.A Surprising Battleground: New York has emerged from a haywire redistricting cycle as perhaps the most consequential congressional battleground in the country. For Democrats, the uncertainty is particularly jarring.Pennsylvania Governor’s Race: Attacks by Doug Mastriano, the G.O.P. nominee, on the Jewish school where Josh Shapiro, the Democratic candidate, sends his children have set off an outcry about antisemitic signaling.Herschel Walker: The Republican Senate nominee in Georgia reportedly paid for an ex-girlfriend’s abortion, but some conservative Christians have learned to tolerate the behavior of those who advance their cause.Striking the right balance — or not — could decide whether Republicans win control of the Senate and capture several governor’s offices in key battleground states.That calculation is complicated by political terrain that varies by state. A winning Republican coalition for J.D. Vance in the Senate race in Ohio — a state that Mr. Trump easily won twice — will most likely require a smaller proportion of independent voters than statewide contests in Nevada, which Mr. Trump narrowly lost twice, political strategists said.In North Carolina, Representative Ted Budd emerged from a crowded Republican Senate primary on the strength of an endorsement from the former president. Mr. Budd carried out a multimillion-dollar advertising blitz that prominently featured Mr. Trump’s backing, but he held few public events and skipped all four Republican primary debates..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.But while Mr. Trump won North Carolina twice, his victory two years ago was by fewer than 75,000 votes out of 5.5 million ballots cast.To like Mr. Trump is to love him, while disapproval is often on par with disdain.Bridget Bennett for The New York TimesAt a rally on Sept. 23 in Wilmington, N.C., Mr. Trump’s first event in the state during the general election, Mr. Budd teased a potential third Trump presidential campaign in 2024.“He made America great, and who knows, folks?” Mr. Budd said to thousands of Trump supporters. “He might just do it again.”But when Mr. Budd was asked at his debate on Friday with Cheri Beasley, the Democratic nominee for Senate, whether he wanted Mr. Trump to open another campaign for the White House, he would not say.“I’m going to exclusively focus on this one right now,” Mr. Budd said of his own race. “We have 32 days on this one. Let’s get on the other side of this and let’s have that conversation then.”Mr. Budd also hedged on his support for Mr. Trump’s false claims that the 2020 presidential election was stolen. Mr. Budd voted to overturn the results after a mob of Trump supporters rioted in the Capitol on Jan. 6, 2021, and signed a letter after the election urging the Justice Department to investigate allegations of voter fraud and other irregularities.In late 2020, Mr. Budd also spread bogus claims that voting machines used in some states came from a company with ties to the liberal billionaire George Soros, according to text messages obtained by CNN that Mr. Budd sent to Mark Meadows, then the White House chief of staff.But during the Friday debate, Mr. Budd said he had voted to overturn the 2020 election in order to “inspire more debate.” Blake Masters won the Republican nomination for Senate in Arizona with the help of Mr. Trump’s endorsement.Rebecca Noble for The New York Times“Debate is healthy for democracy,” Mr. Budd added, without explaining what needed to be debated at the time of the vote. At that point, the Trump campaign had made several unsuccessful court challenges and each state’s Electoral College delegation had already met and cast its ballots.Similarly, in Arizona, Blake Masters won the Republican nomination for Senate with the help of Mr. Trump’s endorsement, which arrived months after Mr. Masters recorded a social media video in which he looked directly into the camera to tell viewers, “I think Trump won in 2020.” At the time, Mr. Trump made clear he was snubbing another Republican candidate who the former president believed had not done enough to support the lie that the election was rigged.But at a debate last week with Senator Mark Kelly, the Democratic incumbent, Mr. Masters agreed that Mr. Biden had been legitimately elected. He said that Mr. Biden had probably won because social media companies suppressed negative news about Hunter Biden, the president’s son.But pressed on whether he thought there had been a problem with the counting of votes in 2020, as Mr. Trump has claimed, Mr. Masters declined.“I haven’t seen evidence of that,” he said.Three days after the debate, Mr. Masters mingled with attendees before a Trump rally in Mesa, Ariz. In a brief interview as he shook hands and posed for pictures, Mr. Masters said he stood by his position on election fraud.Asked which position, Mr. Masters replied, “Both.”“Completely consistent,” he said.Mr. Masters smiled, turned and headed toward the stage where he would soon stand side by side with the former president. More