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Utah Democrats, meanwhile, have painted Mr. Huntsman as a Republican flip-flopper who has walked away from some of his stances in order to pander to GOP primary voters.

The state party released a video parody Monday of Mr. Huntsman’s motocross ad, inserting subtitles over the original footage mocking what they see as his new positions.

Huntsman’s changed positions so quickly over the past few days it’s enough to give Utah voters whiplash,” Wayne Holland, state Democratic Party chairman, told reporters on a conference call.

Mark Meckler, co-founder of the Tea Party Patriots, said Mr. Huntsman is creating “zero buzz” among the grass-roots, fiscally conservative movement that helped propel Republicans to take control of the U.S. House last year. “I don’t think a guy like Huntsman has a chance of getting tea party support,” Mr. Meckler said.

The criticisms underscore the key challenge for Mr. Huntsman: prove to Republican primary voters he’s one of them.

It’s the same challenge he faced this month in New Hampshire, when he canceled the motorcycle rally ride because of rain.

“He is legitimately a motorcycle rider,” said Stephen Talarico, owner of a Harley-Davidson dealership in Manchester, where Mr. Huntsman made a campaign stop. “I think the governors’ approach to the motorcycle side of it is these are his constituents — independent Republicans.”

But not everyone was as easily convinced, saying they would have ridden, rain or shine, to the Laconia rally.

“If you don’t ride up, I wouldn’t vote for you,” Davie Lizotte, a 51-year-old from Epping, said with a grin. “If you’re a hardcore rider, throw your rain gear on and go.”