BIG SANDY, Mont. — Under a nearly cloudless sky on the sun-speckled northern prairie last Tuesday, Jon Tester, this state’s senior senator, had his hands deep inside a 25-year-old grain auger.

In Washington, the White House was letting it be known that President Trump was planning a summertime blitz against Democrats running for re-election in states that he had won, a tour that would surely bring him to Montana, where the president’s margin was 20 percentage points.

Mr. Tester had recently torpedoed the nomination of the president’s personal physician, Ronny L. Jackson, to be his secretary of veterans affairs, incurring Mr. Trump’s wrath — “very dishonest and sick!” the commander in chief thundered on Twitter.

But Mr. Tester, a third-generation lentil and pea farmer trying to make up for a late spring, was far more concerned with a broken shear pin that had stopped his bright red auger, which he needed to raise and store leftover seed from the 1,800 or so acres his family has been working for a century. Another repair job a few days earlier had taken out a fresh chunk of flesh from his famously mangled left hand. (Mr. Tester lost three fingers to a meat grinder as a child.)