BUTTE, Mont. — Jon Tester, the senator who looks least like a senator, sized up a crowd of dozens and got to talking about history.
He joined local veterans last week in a creaky hotel ballroom, with his $12 flattop haircut and scuffed black shoes, and spoke of the copper mines up the road, sustaining the nation in wartimes. He saluted Montana’s tradition of bipartisanship, recalling his work, as a Democrat, with President Trump. “The key word is ‘together,’” Mr. Tester said.
Mr. Trump, the president who behaves least like a president, stood hours later before a crowd of thousands in Missoula, Mont., and got to talking about himself.
He mocked Hillary Clinton’s 2016 slogan (“‘Come Together’ or something”). He commended a Montana congressman for having assaulted a reporter (“my kind of guy”). Occasionally, he drifted to the point.
“The Democrats have truly turned into an angry mob,” Mr. Trump thundered. “And your senator is one of them.”
Then came a shout from the audience. “You love my hair?” Mr. Trump called back, losing the thread again. “Thank you. She knows what to say.””
For decades, “all politics is local” has been the most overworked electoral cliché, well-worn mostly because it was so often true. But in critical Senate races across the country — with vulnerable Democratic incumbents in states that Mr. Trump won easily, like North Dakota, Indiana and this one — Republicans have made a different calculation: In an age of tribal fury and presidential ubiquity in the public consciousness, they believe, all politics is effectively national now. Even in a politically eccentric rural state with an abiding emphasis on local individualism and multigenerational credentials in its elected leaders.
Mr. Tester is a Montana lifer. His opponent, Matt Rosendale, the state auditor, is a former Maryland developer who moved here in 2002.
The result, two weeks before Election Day, has been the central strategic divide across several midterm battlegrounds: a Democrat keeping the focus local, hoping to dissociate from divisive national party figures like Chuck Schumer and Nancy Pelosi; and a Republican eager to make the race a referendum on Mr. Trump and the leftist “mob” opposing him, betting that the risk of a volatile and meandering executive messenger is worth the reward of an energized base.
Perhaps nowhere are the parties’ dueling instincts clearer than in Montana, where both sides acknowledge that Mr. Tester, once considered a solid favorite, is now genuinely at risk.
Mr. Trump has taken an outsize interest in the contest, visiting three times to savage the senator he blames for dooming the nomination of Dr. Ronny L. Jackson, Mr. Trump’s choice to be secretary of veterans affairs last spring. Mr. Tester, 62, the top Democrat on the Veterans’ Affairs Committee, helped thwart the nomination, bringing the glare of a national issue to his own doorstep when he released accusations from Dr. Jackson’s former colleagues alleging dubious professional behavior.
“That’s really why I’m here. It’s not that we need the vote so badly,” Mr. Trump said from the stage at an airport hangar, beneath a tangerine mountain sunset. “I can never forget what Jon Tester did.”
Mr. Rosendale, 58, has staked his bid largely on the force of the president’s personality, presenting Mr. Tester as out of step with Mr. Trump’s priorities — tax cuts, gun rights, a conservative judiciary — in a state that the president carried by 20 points.
“Everything that the president has tried to bring forward, Jon Tester has opposed,” Mr. Rosendale said in an interview after touring a lumber company in Deer Lodge. “The people of this state want to see the president’s agenda completed.”
While many Republicans have hugged Mr. Trump close this year, few have matched the dedication of Mr. Rosendale, who owns a ranch in eastern Montana but has retained an accent that suggests he begins each day with Old Bay-specked mouthwash.
His Twitter profile includes two pictures, both of him with the president. He posts like a fan, tagging virtually every message with #MAGA. He plans to travel the state this week with Donald Trump Jr. and Kimberly Guilfoyle, a former Fox News host who is dating the president’s son.
There is likely no contested Senate seat for which the president will deserve more credit in the event of a Republican win. And if there is one thing Mr. Trump enjoys as much as winning, it is credit.
Still, for months, Mr. Tester had seemed uniquely positioned to hang on, leaning on the centrist reputation and lunch-pail political brand that first carried him to the Senate in 2006.
He is a third-generation farmer from Big Sandy, working his 1,800 acres by tractor. In huddles with colleagues in the halls of the Capitol, he can resemble a retired football lineman discussing investments with his accountants. (Mr. Tester is nearly 300 pounds.) And reporters can rarely resist mention of his signature biographical detail: the meat grinder accident that left him with seven fingers at age 9. (A meat grinder accident left him with seven fingers at age 9.)
At the veterans event in Butte, a short walk from a Democratic field office with a cat who goes by Little Sandy, Mr. Tester deployed the full homespun charm offensive. The senator said the president’s tariff policy “scares the hell out of me” as a farmer. He professed “no love” for the Affordable Care Act, which he voted for, suggesting he was open to changes short of outright repeal. He ceded the microphone to a Trump-supporting veteran who likes Mr. Tester, too.
“I’m somebody born and raised here, somebody who was educated here, somebody who’s been in business here,” Mr. Tester told reporters.
Attendees cheered inside a reception space in the grand, old Hotel Finlen, where brochures advertise a historical guest list of “recent notables” including Charles Lindbergh, Vice President Nixon and “Mrs. Herbert Hoover.”
“He’s not handsome, he’s not pretty, he’s not trying to be,” Norma Duffy, 62, said of Mr. Tester. “None of us Montanans are all that good-looking.”
Generally, the Democratic formula for victory here, in this state of just over 1 million people, has been to keep losses manageable in heavily Republican ranchlands to the east while turning out voters in denser areas out west: state workers around Helena, younger voters in college towns like Missoula and Bozeman, long-tenured labor households around Butte, once known as “the richest hill on Earth.”
Though the state’s last two governors have been Democrats, running for federal office can be thornier, with culturally conservative voters who remain deeply skeptical of the big-government cosmopolitanism they associate with the national party.
Mr. Tester has not cleared 50 percent in either of his victories. His latest race may well turn on how many Montanans vote for the Libertarian candidate, Rick Breckenridge. In 2006, Mr. Tester won by less than 4,000 votes while a Libertarian candidate took more than 10,000. In 2012, he won by about 18,000; a Libertarian earned nearly 32,000.
In this race, some major issues have been perennial Montana flash points, like gun policy and land use. Mr. Rosendale has mocked Mr. Tester for a D-rating from the National Rifle Association; Mr. Tester has hit Mr. Rosendale for previously supporting the transfer of federal lands to the state, an approach Mr. Rosendale now opposes.
But the defining division has been on Mr. Trump, particularly since the confirmation of Justice Brett M. Kavanaugh. Republicans have framed Mr. Tester’s vote against him as an extension of his resistance to Dr. Jackson and other administration wishes.
“He has tried from the outset to make this an election about Trump,” Rick Hill, a former Republican congressman from Montana, said of Mr. Rosendale. “If you were to ask my opinion four months ago, I would have said it might not be the best tactic to take. But it’s put him in position to be able to win.”
Republican leaders had initially viewed Mr. Rosendale as a weak recruit, disappointing party officials who hoped that Ryan Zinke, Mr. Trump’s interior secretary, or Tim Fox, the state attorney general, might run. “We were not terribly optimistic,” Mitch McConnell, the Senate majority leader, said in a recent interview. “But it’s ended up being a dogfight.”
And if most rallygoers last week were plainly there to see the main event, they seemed amenable enough to the undercard. “I guess I’ll vote for him,” Danny Bartley, 24, said of Mr. Rosendale, after learning his name. The president wanted him, after all.
The next day, Mr. Rosendale was still exulting in the reflected glow. “When the president comes to Montana, it brings a level of energy that no one can replicate,” he said in the interview. “It just does.”
But the event highlighted a contrast in how voters tend to consume Mr. Trump’s barnstorming. Local headlines focused largely on the president’s support for Mr. Rosendale. Outside of Montana, most news accounts dwelled on Mr. Trump’s praise for Representative Greg Gianforte for body-slamming a reporter last year.
Mr. Rosendale, whose parents started a small newspaper in Maryland in his youth, was less eager to address that moment. “We’re focused on our race,” he said, declining to say if Mr. Trump was right to praise the assault. “That’s really more background noise for you in the national media.”
It was pointed out that Mr. Trump, not the news media, had said those words.
“I, uh,” he began, before reconsidering. He shrugged a bit, waiting in silence for a different question.