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His boss may be backing Donald Trump, but Republican Lt. Gov. Spencer Cox said he won't vote for his party's nominee unless Trump drastically overhauls his tone and rhetoric.

"If there were some major changes to Trump, I think there's a way many of us could support him, but he hasn't shown any inclination toward those changes or doing things differently, so I think it's a long shot that he will change," Cox said in an interview.

Cox said he hasn't decided who he's going to support in November. He has met with Evan McMullin, who jumped into the race recently, billing himself as a conservative alternative to Trump, and is interested in learning more about him. He has researched Libertarian candidate Gary Johnson. And it is possible, Cox said, that he will write in someone else entirely.

Cox will not vote for the Democratic candidate, Hillary Clinton, and feels as strongly about opposing her as he does Trump.

But Cox does not agree when it comes to Trump with Gov. Gary Herbert, who said last week that he plans to support the Republican nominee, and said that Trump's "unvarnished comments" that have offended many are part of what makes the candidate appealing to many.

"The governor and I are two different people. We've said from the beginning that we are not going to agree on everything," Cox said. "[We] have had many discussions about this and I want to make it clear that I'm not being critical of his decision or the decision of anyone who has felt the need to vote for the Republican candidate. This is one of the most difficult elections I've ever seen where it is such a tough decision for everyone."

Also this week, Jim Bennett, the son of late-Sen. Bob Bennett, said he was leaving the Republican Party because he couldn't stomach Trump as the nominee.

"The Republican Party that was near and dear to my heart for most of my adult life bears very little or no resemblance to the party of Trump," Bennett told MSNBC. "You know, people had called me a RINO, a Republican in name only, and I decided that I no longer wanted to be a Republican even in name as long as Donald Trump is heading the ticket."

The Exodus from Trump among Utah Republicans is indicative of the deeper disenchantment among Utahns and Mormons with the party's nominee.

"[We're] having a tremendous problem in Utah," Trump said last week, speaking to a group of evangelicals. "Utah's a different place and I don't know, is anybody here from Utah?... I didn't think so. We're having a problem."

Cox said there's no easy way to pinpoint what it is about Trump that makes it impossible for him to support the nominee.

"All of it. Where do you start?" Cox said. "I believe in the party of Lincoln, a party that reaches out to others, that is optimistic, that lifts up those that need the most help. I feel he represents the opposite of almost every one of those things I believe the Republican Party has meant for 150 years."

Cox said he also believes the office of the president, whoever holds it, requires a certain dignity and he wants someone who his children can look up to, even if they disagree on policies.

At the Republican National Convention in June, Cox said he was on the fence about whether he would support Trump and hoping to hear something that would help him feel better about the choice. Since then, he said, everything he has heard has pushed him the opposite direction.

"I'm trying to want to vote for the Republican nominee," Cox said. "My life would be much easier if I were able to vote for the Republican nominee. I keep waiting and hoping and looking and not only have I not seen what I was hoping for, it's actually gotten worse, with his attacks on the Kahn family and so on."

Trump lashed out at Khizr and Ghazala Khan, the Muslim parents of a dead Army captain, who challenged him at the Democratic National Convention, suggesting that Ghazala Khan, the soldier's mother, had not been allowed to speak.

Twitter: @RobertGehrke