Paul Krugman says
there aren't enough libertarians in the U.S. to make a libertarian candidate like Rand Paul viable. I am not so sure about the paucity of libertarians, but even so, I doubt that Rand Paul is the best representative of that group.
Similar to Krugman, I would define a libertarian voter as one who leans left on social issues (such as same-sex marriage) and right on economic issues (such as taxes and regulation). I certainly put myself in that camp, and I don't think I am as lonely as Krugman suggests. I meet lots of students with similar views (though, admittedly, Harvard students are hardly a representative sample of voters).
Nonetheless, I think libertarian candidates face several challenges. In particular, the Republican party has traditionally relied on an uneasy coalition of economic and social conservatives. A libertarian candidate would need to put together a very different coalition.
Rand Paul does not seem ready to do that. He has come out opposed to same-sex marriage, for example. He is unlikely to put together a new coalition with that position.
Many libertarian voters I know (including those students) often vote for Democratic candidates because they weight the social issues more than the economic ones. I usually vote for Republican candidates because I weight the economic issues more than the social ones.
One reason is that I don't view the Democratic Party as a leader on social issues. Remember that Bill Clinton signed the Defense of Marriage Act. Barack Obama was against same-sex marriage when he ran for President, and then he "evolved" (aka flip-flopped) on the issue. On this social issue and many others, our elected leaders are really followers. The leaders are the American people.