Ohio Gov. John Kasich has become toxic on the 2018 campaign trail, where his anti-Trump crusading and complaints about the two-party system have sent fellow Republicans scurrying from him.

In Indiana, Republicans running for the Senate are competing to denounce their neighboring governor, and in his own state, some Republicans are eager to put distance between themselves and Mr. Kasich.

“I would rather get some fatal disease than get Gov. Kasich’s endorsement,” said Mike Gibbons, an investment banker who is running against Rep. Jim Renacci in the GOP Senate primary in Ohio. “He is the least popular Republican figure in this state.”

Mr. Kasich was the last man standing in the 2016 GOP primary race against Mr. Trump and has been a striking holdout as much of the rest of the Republican Party has embraced the president.

He’s also criticized fellow Republicans for their handling of the big issues on everything from gun control and immigration to attempting to repeal Obamacare. He even criticized the tax cut package most Republicans have embraced, saying it takes “money out of our kids’ piggy banks.”

“I don’t think either party is answering people’s deepest concerns and needs,” Mr. Kasich said on ABC News’ “This Week” program on Sunday. “We may be beginning to see the end of a two-party system. I’m starting to really wonder if we are going to see a multiparty system at some point in the future in this country.”

Mr. Kasich has also kept afloat the idea of challenging Mr. Trump in the GOP primary in 2020.

That kind of treatment of their party leader has irked Republicans, who are increasingly unified under Mr. Trump.

Rep. Todd Rokita, Indiana Republican, has made opposition to Mr. Kasich a part of the Senate primary in his state. He demanded one of his rivals for the Senate, Rep. Luke Messer, condemn Mr. Kasich over continued 2020 talk.

Mr. Messer countered by demanding Mr. Rokita also condemn Mr. Kasich.

In Ohio, meanwhile, Lt. Gov. Mary Taylor distanced herself from Mr. Kasich and his backing, even as she runs to succeed him in office. She even claimed she hadn’t spoken with the governor in a year — an account Mr. Kasich disputed to Ohio reporters.

Mr. Gibbons, whose who campaign team includes former Kasich 2016 operatives, said Mr. Kasich has never rebounded from his decision not to endorse Mr. Trump at the Republican National Convention in Cleveland.

“I think every Ohioan was embarrassed by what he did,” Mr. Gibbons said. ‘He is like a child, an impetuous child.”

Mr. Kasich’s office did not respond for comment.

Former Rep. Thomas M. Davis III, who served with Mr. Kasich in the House, said his former colleague is frustrated and speaking his mind.

‘There is no question that he resonates with some Republicans and Independents and to others it is a message of apostasy,” Mr. Davis said. “It speaks to the polarized world we live in.”

“He has always been pretty independent,” Mr. Davis said. “For those of us who know and served with John Kasich, that is John Kasich. He has always been his own man.”

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