LAS VEGAS — In 2010, Senator Harry Reid of Nevada beat back a deep-red wave and dire national predictions for his political career when he pulled out a re-election victory against a Tea Party-endorsed candidate. He was a Democratic powerhouse with name recognition, pugilistic instincts and a state political machine long in the making behind him.Twelve years later, Senator Catherine Cortez Masto, who replaced him in Congress, finds herself in a re-election battle in November against the Trump wing of the Republican Party. But Ms. Cortez Masto is not as well known as her Senate predecessor and mentor, the so-called Reid Machine is not as strong as it had been during his tenure and Democrats are facing an even tougher national political landscape.“When you take that all together — this is why Nevada’s Senate contest is one of the most competitive races in the country,” said Mike Noble, a pollster who works in the state.Ms. Cortez Masto, the state’s former attorney general, easily won the Democratic nomination in Tuesday’s primary election. But she remains one of the most vulnerable Democratic senators this midterm season, as she prepares for a general-election contest against Adam Laxalt, a Republican who has embraced former President Donald J. Trump’s baseless claims of a 2020 stolen election.A combination of local, national and personal challenges confront her in a high-profile race — state voting trends that favor Republicans, a national climate working against Democratic incumbents, and her own tendencies to stay out of the limelight and operate behind the scenes.But she and her supporters point to her past hard-fought victories, most recently in 2016, when she beat her Republican rival by 2 percentage points to become the first Latina elected to the Senate.“I’ve always been in tough races,” Ms. Cortez Masto said in an interview in February.Adam Laxalt greeted voters in Moapa Valley, Nev., on Saturday.Joe Buglewicz for The New York TimesIn Nevada, the influential network of seasoned operatives, field organizers and volunteers that has fueled crucial Democratic victories for years is still a major force in the state’s politics. It now includes a newer crop of progressive groups. But the loss of Mr. Reid, who died in December 2021 after a struggle with pancreatic cancer, has been hard felt.President Biden won Nevada by only 2 percentage points during the 2020 election. Ms. Cortez Masto will now have to overcome the president’s low approval ratings and voters’ dissatisfaction with the economy. Nevada, whose sprawling hotel and entertainment industries heavily rely on tourism, was among the states most battered by the coronavirus pandemic, and high unemployment rates and rising living costs have opened Democrats to a constant line of attack from Republicans on crime, jobs and inflation.“In November, voters are going to see the prices at the pump, see the inflation when they go to the grocery store and know that they have Catherine Cortez Masto to thank for that,” said Jeremy Hughes, a Republican who was a campaign adviser to Dean Heller, the former Republican senator.Understand the June 14 Primary ElectionsTakeaways: Republicans who embraced former President Donald J. Trump’s election lies did well in Nevada, while his allies had a mixed night in South Carolina. Here’s what else we learned.Winners and Losers: Here is a rundown of some of the most notable wins and losses.Election Deniers Prevail: Republicans who deny the 2020 election’s result are edging closer to wielding power over the next one.Nevada Races: Trump-inspired candidates captured key wins in the swing state, setting the stage for a number of tossup contests against embattled Democrats.Texas Special Election: Mayra Flores, a Republican, flipped a House seat in the Democratic stronghold of South Texas. Her win may only be temporary, however.The election will largely hinge on who shows up to the polls. Mr. Reid’s political apparatus had been crucial to mobilizing multiracial coalitions of working-class and Latino voters. But sharp drops in Democratic participation in Nevada midterm elections have most recently given Republicans an advantage. The state’s transient population also makes it difficult for political candidates and elected officials to build name recognition.Voters line up outside a polling place in Las Vegas Tuesday.Bridget Bennett for The New York Times“The challenge for everyone on the ticket in Nevada is turnout,” said Representative Dina Titus, a Democrat who is facing her own tough bid for re-election this year for her Las Vegas seat.Mr. Laxalt has largely centered on turning out his base by stirring voter outrage over undocumented immigrants, the economy and pandemic school closures and restrictions. He has already begun to attack Ms. Cortez Masto as a vulnerable incumbent in line with Biden administration policies.The grandson of a former Nevada senator and son of a former New Mexico senator, Mr. Laxalt served as co-chairman of the 2020 Trump campaign in Nevada, and led Mr. Trump’s efforts to overturn the 2020 election in the state. He was endorsed by both Mr. Trump and Gov. Ron DeSantis of Florida, two of the most popular figures in the Republican Party.In a memo released the day after the Tuesday primary, Scott Fairchild, Ms. Cortez Masto’s campaign manager, painted Mr. Laxalt as a corrupt politician and “an anti-abortion extremist” focused on promoting Mr. Trump’s “big lie.” Her supporters see him as a flawed candidate, pointing to his failed bid for governor in 2018 and his attempt to block a federal investigation as attorney general into some of his wealthiest donors, including the Koch brothers.At campaign rallies and in interviews with Fox News and on conservative podcasts, Mr. Laxalt has repeatedly sought to tie Ms. Cortez Masto to Biden policies, criticizing her on crime, inflation and immigration. In a statement, John Burke, communications director for the Laxalt campaign, called criticism from his Democratic opponent a distraction from Ms. Cortez Masto’s role in the “current economic catastrophe.”“Our state wants change and Nevadans know it’s impossible to get it with her,” he said.Despite the change in Nevada’s political environment, many Democrats still see a playbook for success for Ms. Cortez Masto in Mr. Reid’s successful 2010 run for a fifth term against Sharron Angle, a former state lawmaker who pushed voter fraud claims and harsh anti-immigrant rhetoric long before Mr. Trump did.Understand the 2022 Midterm ElectionsCard 1 of 6Why are these midterm races so important? More