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.