In perhaps the oddest quirk of a decidedly erratic year, Mr. Kander may be benefiting from Mr. Trump’s anti-establishment message. Mr. Blunt, who has served in Congress since 1997 and whose family is chockablock with lobbyists, is the archetypal boogeyman Mr. Trump has attacked in his assault on Washington insiders.

Mr. Kander often finds Trump and Clinton supporters at his campaign events — people who fight among themselves, he said, even as they share support for him.

“There are people who will choose to vote for Donald Trump because they want to shake up that conversation,” Mr. Kander said in an interview in St. Louis. “They are not going to go to that next line on the ballot and vote for somebody who they know is exactly who Donald Trump is talking about.”

Until 2004, Missouri was an even more reliable presidential bellwether state than Ohio. But growing homogeneity outside its larger cities has made it more reliably Republican on the presidential level. Still, it remains a state where voters have a tendency to pick Democrats for other statewide offices.

“The misconception about Missouri is that it is a red state,” said Ken Warren, a professor of political science at St. Louis University. “They don’t like Democrats at the top of the ticket because they are seen as from out of town. But most of our statewide offices are held by Democrats.”

It is a reality that Mr. Blunt seems to be just starting to confront, much to his party’s chagrin. “It’s a competitive race, like Missouri races usually are,” he said in an interview at the local Republican headquarters here, where he nibbled on a depressing-looking bagel grabbed off a buffet, the sort of campaign sustenance typical of the exhausting final weeks on the road. “I’m confident of where we are. But not overly confident.”

As of mid-October, Mr. Blunt led Mr. Kander 46 percent to 44 percent, a three-percentage-point drop since August. Democrats need to gain five seats to retake control of the Senate — four if Hillary Clinton wins the presidency, which would give Tim Kaine, her vice president, a tiebreaking vote. Both parties now, surprisingly, view Missouri as a crucial state in that battle.