In the Democratic primary, Andy Beshear, the state attorney general, pulled out a win with 38 percent of the vote, beating out a more conservative candidate and a more liberal one. Not all Democrats agreed that Mr. Beshear would be the best candidate to beat Mr. Bevin. But Mr. Beshear can make the case that he has already battled with the governor as much, and as fiercely, as anyone.

As attorney general, Mr. Beshear has filed multiple lawsuits against the Bevin administration, over service cuts, the pension overhaul and the governor’s attempts to find and punish teachers who staged sickout protests. Mr. Bevin, meanwhile, has frequently attributed the state’s problems, like the drastically underfunded pensions, to the neglect and mismanagement of previous administrations — and even ordered an investigation of the administration of Steve Beshear, his immediate predecessor, a Democrat who served two terms and also happens to be Andy Beshear’s father.

It would be difficult to imagine a starker contrast, one that will surely be drawn in a campaign that many expect to be nastier and more divisive than any in recent memory. That, to many, is the conundrum.

“Sometimes I feel like a man without a party,” said Reggie Dickerson, 54, a pipe fitter from eastern Kentucky. Mr. Dickerson, as a strong union man, was a longtime Democrat, but switched his registration to Republican over the issue of same-sex marriage. Then he switched back to support the conservative Democrat in this year’s primary. And he is now switching back again, largely over the issue of abortion.

“An east Kentucky Democrat is not even close to a Louisville or Lexington Democrat,” he said, contrasting his evangelical convictions with the secular outlook of many Democrats in the state’s big cities.

And how close does he see himself to a Republican like Mr. Bevin, who champions right-to-work laws and the privatization of government services? “Not real close either,” Mr. Dickerson said.

The current era of all-or-nothing partisanship is an awkward fit for Kentucky. It would be easy to take the state these days for an unquestioned stronghold for Republicans, given their supermajorities in both houses of the Legislature and the fact that Republicans hold all but one of the state’s seats in Congress.