G.O.P. Infighting and Democratic Mischief Animate Montana Senate Race

In one of the nation’s top Senate races, the most important candidate might be one who hasn’t actually entered the contest.

The scramble to challenge Senator Jon Tester, Democrat of Montana — already a heated battle with profound national implications and the acute intensity of a family drama — has increasingly focused on Representative Matt Rosendale, an anti-abortion, election-denying Republican agitator.

Both parties are using him as a pawn in their electoral chess match: Establishment Republicans, who have aligned behind Tim Sheehy, a wealthy businessman, are trying to keep Mr. Rosendale out of the race, while Democrats appear to be helping clear a path for his arrival.

Mr. Rosendale’s entry appears imminent. On Thursday, he said on a podcast that he had told Senator Steve Daines, a fellow Montanan who oversees the Republican Senate campaign arm, that he was going to run for Mr. Tester’s seat.