It's no secret that the Republican party is short on heroes at the moment. Ted Cruz's recent audition fell a little flat (his voice and hair are probably more suited to a Pixar villain, anyway). Marco Rubio seems to have gotten his cape stuck in the establishment escalator. Chris Christie is still at the mercy of a vigorous training schedule, and Jeb Bush hasn't even entered the phone booth to change.

That leaves Rand Paul. Rand-Man! Able to leap tall filibusters (real ones) in a single bound! Lusty defender of the spied-upon and drone-targeted, the casual drug user and reluctant interventionist! For a while, he even had a costumed sidekick: "the Southern Avenger", a pro-secessionist, anti-Lincoln former talk radio host turned social media consultant known to occasionally don a Lucha Libre-style confederate flag mask.

And that kind of sums up the strengths and weaknesses of Rand Paul for president. He comes with a bright and shiny set of opinions on marquee issues that are just far enough ahead of the curve to seem brave. He also comes with the baggage of a libertarian movement that has, for generations, been a home to passive-aggressive racism and medium-to-high levels of kookiness. He talks a good game on the general principles of civil rights and liberty, but policy specifics (and staffing) are his kryptonite.

True, that could be said of almost any politician who can string together enough sentences and Super Pacs to make it to the Senate. Thus far, the main argument for Paul becoming a top-tier candidate in 2016 seems to be, "Why not?" For his part, Paul is doing all the things a potential candidate needs to do to be considered possible: showing up in Iowa and New Hampshire, mostly, but also proposing flashy but doomed legislation ("Air Travelers' Bill of Rights", anyone?) and standing in front of as many cameras as possible (he's in the October Vogue).

But, for real, what are the odds?

A few months ago, Nate Silver slogged through some high-level scenarios that could produce a Rand nomination and pronounced the less-than-ringing endorsement of "better than the 20-to-1 numbers that some bookmakers have placed against him".

Today, those odds seem to have improved. Rand's anti-drone filibuster endeared him to many liberals disenchanted with Obama's surveillance state and his anti-interventionism resonates well with a war-weary and suspicious American public. What's more, the Tea Party's floundering and steady flow of crappy spokesfolk (Michele Bachmann! Herman Cain!) has only made it more vulnerable for the right person to harness it. Though support for the leaderless movement is down to 22%, from a high of 32% in 2010, getting a lock on almost a quarter of potential conservative voters who claim dissatisfaction with the traditional GOP could be the golden ticket for a different kind of candidate. Rand stands a better chance than most at unlocking that support.

In imagining a Paul presidency, that's about as far as I get … before the reality bells start ringing.

His admirable support for privacy rights and for ending the drug war, while attractive to many on the left, simply could not outweigh his extreme – and extremely unpopular – opinions on other civil rights issues: in March, Paul proposed the Life at Conception Act, which would effectively outlaw all abortions and end the protections of Roe v Wade by claiming that Congress has power under the 14th amendment to declare when life begins. Fifty-two percent of Americans believe that abortion should be legal in "some circumstances", and another 26% say it should be legal in "all circumstances". And while a majority of Republicans (63%) believes that abortion should be illegal, candidates have paid a high cost for total inflexibility on the issue.

In the wake of the Sandy Hook massacre, Rand introduced legislation to "nullify" Obama's executive orders on guns despite their popularity with the public. Rand used the language of libertarian political philosophy to justify the bill – "we will nullify anything the president does that smacks of legislation" – an argument that liberals and moderates burned by Bush's heavy-handed executive privilege might like.

But how to separate that feisty populism from the gun policies Rand does support? They are straight-from-the-NRA loony tunes. He wants "concealed carry" for teachers and he has fundraised off a tinfoil-wrapped conspiracy that the UN is coming for American's guns. A letter sent under his name last May went full black-helicopter:

Ultimately, UN bureaucrats will stop at nothing to register, ban and CONFISCATE firearms owned by private citizens like YOU. So far, the gun-grabbers have successfully kept many of their schemes under wraps. But looking at previous attempts by the UN to pass global gun control, you and I can get a good idea of what's likely in the works.

On economic issues, Rand has some schemes of his own, like a de facto halving of the top tax rate via a 17% flat tax. He would double-down on the kind of 1%er-friendly proposal that worked out so well for Mitt Romney. The flat tax is also Rand's overture to the LGBT community: prior to the supreme court's Defense of Marriage Act (Doma) decision, Rand tried to shade his affirmative belief in "traditional marriage" by asserting that his flat tax "wouldn't have marriage as part of the tax code". Getting the government out of the marriage business is a nice idea, but given the entrenchment of marriage in all facets of our civil society, I'm not sure "here's a flat tax" cuts it for same-sex couples: sorry about your oppression, have a regressive policy proposal!

Paul's budget proposal, presumably the one he would run on, also eliminates the departments of Housing and Urban Development, Energy, Commerce and, most radically, the Department of Education. He might find sympathy among those with a generalized distaste for government spending, but under the purely philosophical or economic reasoning are Paul's uglier motives (the economic motives are already pretty ugly, by the way). As he put it in a debate during the Kentucky Senate race:

I don't like the idea of somebody in Washington deciding that Susie has two mommies is an appropriate family situation and should be taught to my kindergartener at school. That's what happens when we let things get to a federal level.

But, hey, flat tax, am I right?

The list of unworkable and/or unwinnable policies goes on. On the flip side of his anti-military intervention rhetoric is his opposition to foreign aid for anyone. He's fond of saying that the US "shouldn't give a penny to those who would burn our flag" or persecute Christians, but that rhetoric dodges key facts: first, the No 1 recipient of US aid is Israel; and second, the money that goes to Iraq, Pakistan, and Egypt likely keeps the number of flags burned down.

But let's try to put all that aside. Wait, I can't! Trying to seriously investigate what a Paul presidency would bring carries with it a suspension of disbelief that makes all things possible. When you talk to libertarians about how Paul might actually manage to push his radical policies through, were he to become president, they say things like, "use the bully pulpit" (works so well for Obama) and "ride on the vast wave of support that brought him to office". In other words, if you're living in the America that elects Rand Paul, getting the votes to privatize Medicare (actual Paul proposal) is the least of your worries. You'll be too busy dodging cars on the mythical Nafta superhighway (an actual Paul belief).

The real asset Rand Paul brings to the table is a certain brittle charisma and veneer of normalcy. He has played nicer with the party establishment than Cruz. He has engaged, awkwardly, with minority voters – though his actual policies are a mismatch with both Hispanics and African Americans.

Rand Paul also benefits greatly from the counter-example set by his fiery and diminutive father, Ron, whose unfortunate sartorial choices and blatant wingnuttery make Rand seem both suave and moderate by comparison. His suits seem to fit him and he does not, for example, talk loudly about hoarding gold. A Center for Responsive Politics investigation found that Rand is less Rumpelstiltskinian than his father, in practice as well as rhetoric; while the elder Paul has north of $500,000 invested in gold, Rand's largely paper holdings are "more in line with the general public".

And if the Southern Avenger looms as one threat to Paul's candidacy, this undercover normalcy is another. Paul is libertarian enough to attract some of the fringe; indeed, he is the fringe. But when it comes to risking his own skin, he plays it safe. He is not a superhero, he is a costumed non-adventurer.

Whether this combination of libertarian flair and basic conservatism, in a personal sense, is his salvation (exactly the kind of mold-breaker the GOP needs!) or his downfall (not a real Republican, or real anything) remains to be seen. I suspect that, eventually, he will have to lean to one side or another. At that point, he will cease to be a unicorn and become just another dark horse.