Mr. Hawley, who won more votes than anyone else on the ballot here in 2016, is confident that voters will overlook the association in favor of his positions on issues like jobs, wages and immigration. Mr. Hawley has avoided making public appearances with Mr. Greitens in recent weeks, even skipping some party events. And his decision to call for Mr. Greitens to step down is likely to help.
Even with the unexpected boost of the governor’s scandal, Democrats will need voters here to show some of their old independence. Mr. Trump won the state by a larger margin than any presidential candidate in decades, but other statewide races in 2016 were closer, including that of the state’s senior Republican senator, Roy Blunt, who eked out another six-year term by less than three percentage points.
And the situation could be worse for Republicans. The scandal is playing out in April, rather than this fall, when midterm voters will be making up their minds. With political pressure on Mr. Greitens intensifying, he could resign quickly and be a distant memory by then.
Since 2016, Ms. McCaskill has put a heavy emphasis on rural Missouri, once reliably Democratic country where she grew up and hopes to retain some of her old appeal. Of 50 town-hall-style meetings she held last year, most were scattered around rural Missouri. The point, her allies say, was to show that Ms. McCaskill shows up, unafraid to take hard questions from her critics about her record.
Mr. Hawley and other Republicans have tried to hammer away at that image. To hear them tell it, Ms. McCaskill, who has held one public office or another here since 1983, has long since lost her way. Too liberal. Too rich. Too coastal for Missouri.
In Hannibal, the childhood home of Mark Twain, Mr. Hawley made sure to point out that Ms. McCaskill was soon bound for another cultural landmark, Hollywood, for a multimillion-dollar fund-raiser with Barack Obama and Steven Spielberg. The modest crowd that had gathered in the warehouse of a cement company booed.
For now, Republican strategists here are resigned to Mr. Greitens’s impact on the race. A quick resolution would be best for Mr. Hawley, said Scott T. Rupp, a member of the state’s public service commission and a former Republican state senator. But whether the governor will knuckle under is anyone’s guess.
“It’s looking at a crystal ball to see how much,” Mr. Rupp said.