Each candidate has been heaping praise on Mr. Trump and attacking the others as insufficiently loyal to the president. The Associated Press estimated last week that roughly $45.7 million had been spent in the race.

Last week, Vice President Mike Pence endorsed Ms. Black, who could become the state’s first female governor if she wins in November.

The two-way race on the Democratic side between former Mayor Karl Dean of Nashville and State House Minority Leader Craig Fitzhugh has been placid in comparison; Mr. Dean is favored to win.

The Tennessean, a local newspaper, estimated that Mr. Dean had raised 15 times as much as Mr. Fitzhugh, and spent four times as much.