SEATTLE — Ahead of their first election in Washington State, Carys Hagen and her partner, Shaw Lenox, stumbled upon a rally held for Senator Patty Murray, a Democrat, on a stage in the corner of the Seattle Center.“Like, don’t love,” said Ms. Hagen, who identifies as a socialist, summing up her feelings about Ms. Murray after listening to the opening minutes of her stump speech. “But I’ll take ‘like’ any day of the week.”For Ms. Murray, who is facing a surprisingly tough race after three decades in Congress, the lack of enthusiasm is reason for concern.“If they just — ‘Oh, Patty’s fine, she always has been’ — that’s when elections get really tight,” Ms. Murray said in an interview. “Because we need Democrats to vote.”Since she first won her seat in 1992, Ms. Murray has steadily climbed the ranks to wield heavy, though understated, influence as a senior member of leadership and the chairwoman of the Senate committee that focuses on health, labor and education. Should she win a sixth term next week, she will be the fourth most senior senator and in line to be the top Democrat on the powerful Appropriations Committee that controls government spending.But her re-election hinges in large part on voters like Ms. Hagen putting aside their frustrations with a national party that has fallen short of some of its most expansive policy ambitions and casting a vote for Ms. Murray, whom many of them have come to regard as a fixture who will be there no matter what.She is working to fend off a surprisingly stiff challenge from Tiffany Smiley, a Republican who is mounting her first run for public office after years as a nurse, veterans affairs advocate and caregiver.Ms. Murray has spent the final weeks of her campaign trying to ward off complacency within her party.“We are a Democratic state,” she told a group at a “pro-choice, pro-Patty, pro-coffee” event at a local Seattle coffee shop. “If people vote.”In an open primary this year, Ms. Murray easily bested Ms. Smiley, winning more than 52 percent of the vote to Ms. Smiley’s nearly 34 percent, and she is still seen as the favorite to prevail. But Republicans have continued to funnel millions of dollars into Washington State, Ms. Smiley has out-raised the incumbent senator and polls have tightened in recent weeks, rattling some Democrats.The State of the 2022 Midterm ElectionsElection Day is Tuesday, Nov. 8.A Pivotal Test in Pennsylvania: A battle for blue-collar white voters is raging in President Biden’s birthplace, where Democrats have the furthest to fall and the most to gain.Governor’s Races: Democrats and Republicans are heading into the final stretch of more than a dozen competitive contests for governor. Some battleground races could also determine who controls the Senate.Biden’s Agenda at Risk: If Republicans capture one or both chambers of Congress, the president’s opportunities on several issues will shrink. Here are some major areas where the two sides would clash.Ohio Senate Race: Polls show Representative Tim Ryan competing within the margin of error against his G.O.P. opponent, J.D. Vance. Mr. Ryan said the race would be “the upset of the night,” but there is still a cold reality tilting against Democrats.If Ms. Smiley — who is 41, the same age Ms. Murray was when she first announced her run for office — were to prevail, she would be the state’s first Republican senator in more than two decades.Underscoring the severity of Ms. Smiley’s challenge in what political handicappers considered a safely Democratic seat until this month, multiple high-profile surrogates have trekked to Washington to rally for Ms. Murray and try to galvanize Democratic voters who they fear might fail to turn out for midterm elections in a typically liberal state.Tiffany Smiley, center, a nurse and veterans affairs advocate, is challenging Ms. Murray.Chona Kasinger for The New York TimesVice President Kamala Harris headlined a donor gathering in the state last week, as well as an event highlighting investments from the $1 trillion infrastructure law. Senator Elizabeth Warren of Massachusetts came to rally supporters for Ms. Murray, a cerebral politician more comfortable in a private negotiation than at a raucous rally.“Patty is not the first person to jump into the spotlight; she’s not the loudest in high-volume debate,” Ms. Warren said in an interview before she walked out with Ms. Murray to Dolly Parton’s working woman’s anthem, “9 to 5.” “But she is effective — anyone who underestimates her is going to find out that they’re on the losing end.”Ms. Murray, 72, has also made a point of crisscrossing the Seattle suburbs and other parts of the state to connect with local leaders and ensure that her core Democratic supporters are turning out to vote. On a gray, drizzly Friday before the rally, she shuttled from a meeting with leaders at a historic Black church to visits with Asian American political leaders and businesses in the city’s international district.In prepared remarks that tick through her legislative accomplishments, she revisits the themes that helped pave her path to Washington three decades ago: the lore of how a male legislator dismissed her as a “mom in tennis shoes” — a slight that she adopted as her campaign calling card — her desire to protect women’s rights and a push to provide affordable health care.She has also focused on the Supreme Court’s decision to overturn Roe v. Wade, the landmark decision establishing a right to an abortion, and vowed to codify it into a law — a message that has resonated in the deep-blue suburbs and cities like Seattle.“We had this assurance for 50 years that we could make choices about our bodies,” said L’Nayim Austin, 51, who brought her 10-year-old daughter, dressed as a suffragist, to see Ms. Murray speak. “It’s infuriating.”Senator Elizabeth Warren, left, campaigned with Ms. Murray in Seattle in late October.Lindsey Wasson for The New York TimesMs. Murray has focused her campaign on turning out Democratic voters and supporting reproductive rights.Lindsey Wasson for The New York TimesAt her campaign office, where there are well-worn posters from previous campaigns scattered around, Ms. Murray described the election as challenging because “this time I have someone who isn’t telling people who she really is, and that’s much harder — she’s trying to look moderate, be conservative without telling anybody.”Ms. Smiley, who has pointedly noted that Ms. Murray once made a speech on the Senate floor praising her, has distanced herself from some conservative stances, saying she will not support a federal ban on abortion access or cutting back Social Security benefits. She has centered her campaign on reducing federal spending, addressing crime and increasing security at the nation’s southern border.And pressed in a recent interview, she asserted that President Biden is the nation’s “legitimately elected president,” though earlier in the campaign cycle, she dodged questions about whether he had been legitimately elected.That has led Ms. Murray and her allies to frame Ms. Smiley as aligned with the Republican Party’s far-right extremists, airing ads evoking the Jan. 6 riot and the prospect of cuts to social safety net programs. Ms. Smiley has accused her opponent of relying on political talking points to hide an ineffective policy record.“Maybe some of Senator Murray’s intentions are good, but we can’t base policy off of intentions,” Ms. Smiley said in an interview aboard her campaign bus, where she criticized many of Ms. Murray’s policies. “It’s very, very dangerous. Policy has to be based off of results.”Supporters have also connected with Ms. Smiley’s emotional recollection of her years of caregiving and advocacy, after her husband, Scotty, was blinded in a suicide car bomb attack in Iraq and became the first blind active-duty officer in the Army.At a rally kicking off her bus tour across the state, Ms. Smiley held back tears as she talked about her husband’s encouragement for her political campaign, reiterating a pledge to work so “that our children have a country worth giving their eyesight for” as the crowd murmured and cheered in approval. She will linger after events to warmly embrace supporters and pose for selfies, thanking them for their prayers ahead of the election.“She’s probably the one and only person maybe in the state who can beat Patty Murray,” said Angela Dabb, a small-business owner and Republican who attended an event on Ms. Smiley’s bus tour at Nana’s Southern Kitchen, a restaurant in Covington that boasted fried chicken and catfish. “I was in tears — and so when a politician can move you like that, you know it’s coming from their heart.”Supporters of Ms. Smiley have connected with her emotional recollection of caregiving and advocacy, after her husband was permanently blinded in a suicide bomb attack in Iraq.Chona Kasinger for The New York TimesA crowd of more than 100 people applauded Ms. Smiley as she kicked off her bus tour in Maple Valley, Wash.Chona Kasinger for The New York TimesAt stops along Ms. Smiley’s bus tour, attendees described frustration with years of Democratic control in their state and across the country. For multiple voters, it was the first time they had decided to volunteer for a campaign and attend events, seeing a glimmer of hope that Republicans could not only claim a seat in the Senate, but also flip at least one in the House.Ms. Smiley, for her part, has also worked to weaponize Ms. Murray’s decades on Capitol Hill, riffing off Ms. Murray’s own motto to brand herself “a new mom in town.” At a bar in Maple Valley a short drive outside Seattle, where she began the bus tour, a raucous crowd of more than 100 people cheered and applauded as Ms. Smiley appeared with her husband, accompanied by Senator Joni Ernst, Republican of Iowa, and a soundtrack of Americana classics.They whooped and laughed as Ms. Ernst joined other national Republicans in lampooning Ms. Murray’s more taciturn affect, noting “I don’t know that I’ve seen her smile once” and calling for a change in representation.But Ms. Murray remained adamant that there was more for her to do in the Senate.“When I was running before, it was — we had no voices in the Senate, there wasn’t anybody in the rooms who could say what we needed to say,” she said, reflecting on her first campaign, in what would become known as the “year of the woman.” “I’m now in that room, but I need to be in that room by being elected.”Ms. Smiley’s supporters described frustration with years of Democratic control both in their state and across the country.Chona Kasinger for The New York Times More