During the interview, with CNBC's Kelly Evans
, Paul yawns, interrupts Evans and at one point motions for her to be quiet with a finger to his lips.
He also reproaches her for a "slanted" interview that he says "got no useful information because you were argumentative, and you started out with so many presuppositions that were incorrect."
Paul, who is an ophthalmologist, also asserts that he's heard of cases where vaccines have caused "profound mental disorders."
"I've heard of many tragic cases of walking, talking, normal children who wound up with profound mental disorders after vaccines," Paul said. "I'm not arguing vaccines are a bad idea. I think they're a good thing. But I think the parents should have some input."
Asked for evidence of those claims, Paul campaign spokesman Sergio Gor didn't address them and instead said that while Paul largely supports vaccines, "many" should be voluntary.
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"Dr. Paul believes that vaccines have saved lives, and should be administered to children. His children were all vaccinated. He also believes many vaccines should be voluntary and like most medical decisions, between the doctor and the patient, not the government," he wrote in an email to CNN.
On Tuesday, Paul further clarified his stance, saying he didn't say vaccines caused disorders.
"I did not say vaccines caused disorders, just that they were temporally related -- I did not allege causation. I support vaccines, I receive them myself and I had all of my children vaccinated," Paul said in a statement. "In fact today, I received the booster shot for the vaccines I got when I went to Guatemala last year."
The flap, however, suggests that Paul is still struggling with many of the same issues that have caused GOP operatives to view his likely presidential bid with some skepticism. His staff has long been aware of a perception that he's thin-skinned when met with criticism, and while his pointed responses are typically delivered with clear intent — as with when he attacked New Jersey Gov. Chris Christie as the "king of bacon" — they could complicate his personal appeal to voters, especially if he's pitted against a female candidate.
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And though Paul has largely avoided such controversial topics in his effort to become more attractive to mainstream Republicans, they're nothing new for him and his father. Former Rep. Ron Paul said during his presidential run
that "people have had some very, very serious reactions" from vaccines, and Paul is a member of a physicians' group
that espouses the belief that vaccines can cause autism. Paul will be asked to answer for those past comments, and any future comments he makes, that are outside the mainstream.
Former Rep. Michele Bachmann may serve as a cautionary tale. She faced a firestorm of criticism for similar comments concerning the alleged negative impacts of vaccines during her 2012 presidential run. Her suggestion that vaccines can "put little childrens' lives at risk" during a debate contributed to growing skepticism surrounding her campaign, and an ultimately damning perception of her as too far outside the mainstream to represent the party.