Victor Marx, a Christian ministry leader, martial arts black belt and Republican nominee for governor of Colorado, knows how to weave a wild story. There is the one about how his stepfather forced him to kill a man at age 7. Or his claim that he cast a demon out of a teenage girl. Or his accounts of dodging mortar fire in Iraq to rescue civilians from the Islamic State. Mr. Marx’s biography, from an abusive childhood in Mississippi to commando-style ministry missions, is the centerpiece of his long-shot run to become Colorado’s first Republican governor in two decades.

But his outsized, sometimes hard-to-verify claims have made his campaign a late-night punchline and splintered Colorado’s beleaguered Republican Party. Grassroots conservative evangelicals have embraced Mr. Marx, who has never held elected office, as a spiritual warrior. But some establishment Republicans call him unqualified and say that his candidacy could be a body blow in a once-purple state where Republicans hold no statewide office. “He is not fit to be the governor,” said Dick Wadhams, a former Colorado Republican Party chairman who plans to vote for an independent.

Rep. Lauren Boebert, a far-right Republican, has endorsed Mr. Marx. But most major Republicans have declined and avoid talking about him. Mr. Marx’s supporters say they like him precisely because he is not a regular Republican politician. “It’s an insurgency into the state — a well thought-out plan to take over,” he said. “A takeover by the Socialist Party. I completely believe that.”

Mr. Marx is finding support at biker bars, tailgate parties and in church pews, where working-class voters and evangelicals say they are fed up with Colorado’s spiraling home prices, homelessness and liberal policies. “Tell me a story from your childhood that you didn’t embellish,” said Thayne Brenkman, a construction contractor. “That part doesn't matter. These other people running are demonic.”