On Monday, likely 2016 presidential candidate Rand Paul stuck his foot in his mouth on, of all issues, vaccinations. Despite zero credible evidence that vaccines cause autism, Paul said that he'd heard of "many tragic cases of walking, talking normal children who wound up with profound mental disorders after vaccines." Then, on Tuesday, tape surfaced of Rand Paul linking vaccines to the rise of martial law in the US during a 2009 interview with conspiracy theory site InfoWars: "the first sort of thing you see with martial law is mandates, and they're talking about making [the flu vaccine] mandatory."

This is pretty shocking stuff, even given that other politicians have been busy saying embarrassing things about vaccines. But it tells us a lot about the biggest hurdle to Paul if he decides he wants to win the 2016 Republican primary — Rand Paul.

Paul's Achilles heel is his reputation in the Republican Party as an undisciplined ideologue, a candidate more concerned with libertarian purity than winning national elections. So on days like Tuesday, when he pops off on TV, it seems like he can't help himself from risking confirming the GOP's worst fears about him.

Rand Paul's vaccine comments hurt him where he's most vulnerable

If he decides to get into the 2016 race, he will need to win over party elites. Some go so far as to say he has to win the "invisible primary," the name political scientists have given to the process by which elites inside the GOP — activists, donors, local party officials, and the like — choose who to support in the eventual race.

Paul's political project is incredibly ambitious. He needs to sell his vision of a restrained foreign policy and a minimally intrusive federal government to a party that traditionally believes in aggressive interventionism abroad and strict Christian morality at home. That means Paul already faces an uphill battle among really important constituencies inside the GOP.

To make matters worse, Paul has a dad problem. His father, former Congressman Ron Paul, wasn't just a fairly purist libertarian: he also has a reputation for kookiness and troubling extremism. During the elder Paul's 2008 and 2012 runs for the presidency, journalists discovered a number of shockingly racist newsletters published under Paul's byline. More recently, the Ron Paul Institute (his post-Congress project) posted an article suggesting the Charlie Hebdo shootings may have been a secret US government plot. This history has alienated Ron Paul from mainstream libertarian institutions like the Cato Institute, which emphatically do not share his views on these topics.

The younger Paul not only needs to convince skeptical Republican elites to buy his worldview — which is inspired by the same school of thought as his father's — but he also has to get distance between himself, his father, and his father's ties to outright conspiracy theorists. Even a whiff of that kind of weirdness could turn off even sympathetic Republican elites.

And that's why this vaccine comment is such a big mistake. Paul isn't just aligning himself with an unscientific, deadly conspiracy theory, though he is. He's also aligning himself with exactly the kind of fringe characters — anti-vaxxers — that conjure up Ron Paul's worst excesses. Indeed, Ron Paul has also expressed sympathy for the anti-vaccine cause.

Paul has a history of screwing up like this

In a later comment sent to reporters, Paul's office reiterated the senator's support for vaccination — though it fell short of actually outright denying a link between vaccines and autism. But even if they manage to walk back this particular gaffe, Paul has a habit of slipping up in ways that could reinforce Republican elites' fears about his candidacy.

Like the vaccine incident, these past examples tend to involve either Paul saying something that smacks of extremism or associating himself with people with pretty troubling pasts. All of them were reasonably high-profile:

Before armed anti-government rancher Cliven Bundy opened his mouth about the great life " the Negro "had under slavery, Paul praised Bundy for starting an " After the Charlie Hebdo shootings, Paul suggested restricting Muslim immigration to France and the US as a response. "You've got to secure your country," he said. "And that means maybe that every Muslim immigrant that wishes to come to France shouldn't have an open door to come." A Paul aide, Jack Hunter, used to perform as a radio shock jock named The Southern Avenger, who wore a luchador mask emblazoned with the Confederate flag. While Hunter has (persuasively) disavowed the Southern Avenger's shtick, he resigned his post after Alana Goodman's report on his past kicked off a media firestorm in the summer of 2013. During his original run for Senate in 2010, Paul expressed philosophical opposition to federal desegregation of private businesses in the 1964 Civil Rights Act. "I think a lot of things could be handled locally," Paul said, adding that "I think it's a bad business decision to exclude anybody from your restaurant — but, at the same time, I do believe in private ownership." Paul has since denied any opposition to the Civil Rights Act.

Opposition to the Civil Rights Act, linking Muslim immigration to terrorism, and ties to people with questionable histories on racial issues — each of those things could raise real concerns among elite Republicans. While no single mistake would kill Paul's candidacy, looking at all of these gaffes in one place isn't pretty.

What's really terrible about this is that Paul, and his staff, know that he's vulnerable to the criticism of being outside of the Republican mainstream — and they've worked really hard to address that.

his gaffes may help convince Republican elites that the extremist is the real Paul, and the moderate merely a mask

Nowhere is this more obvious than on foreign policy, Paul's biggest substantive disagreement with the rest of the party. Paul's October speech on world politics cleverly reframed his critiques of Republican neoconservatives as criticisms of Obama's foreign policy. His filibuster against drone strikes, which garnered real support from his colleagues on the Hill, appears to have been fairly popular. His opposition to NSA spying is on the right side of public opinion; Paul has even managed to use the anti-NSA campaign to expand his email list of potential volunteers and supporters for 2016.

Paul's out-front stance on criminal justice reform has also worked surprisingly well. Though Republicans have traditionally stood for harsh punishments and strong police powers, Paul has stood up against police militarization, mandatory minimums, and stripping voting rights from felons. Why isn't this hurting Paul? In recent years, leading conservatives have become more and more sympathetic to softening up the legal system — a trend Paul appears to have read correctly and coopted.

What worked for Paul in both of these cases is that he took a traditionally libertarian issue and made it palatable to Republican ears. He did this by taking moderate, cautious, and reasonable stances where a more hardline libertarian (say, his father) would have been uncompromising.

Instead of opposing all foreign wars, vow only to support them "when vital American interests are attacked and threatened." Instead of demanding the feds legalize pot immediately, call for federalism on drug policy.

This incremental boundary pushing is how Paul wins. But every time he does something like flirt with anti-vaxxers, this positioning comes across less like principled moderation and more like dishonesty. Paul wants Republicans to think his nuanced positions are his actual views. But his gaffes may help convince Republican elites that the extremist is the real Paul, and the moderate merely a mask.

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