Consider all the other issues. For example, with Rand Paul as President, the GOP would certainly control the White House, and House of Representatives, very likely have a 6-3 majority on the Supreme Court within a few years (depending on Justice Ginsberg) ... they'd need only the Senate for one-party rule.
Many, many other things would happen that you probably would not like.
More than that, though, if Rand Paul actually got the nomination -- which he almost certainly won't -- and went on to win the general election, that would potentially be a lot bigger than one minor victory in the constant right-vs-left tug-of-war over American government. It would be a political realignment, because the coalition Rand Paul would build and the platform he would run on are not the traditional Republican coalition and platform.
It could be the start of America actually having a pro-liberty party. That tradeoff might be worth it even for folks on the left who lean libertarian.
I'll take small government over monolithic Authoritarianism any day.
Http://time.com/3759378/rand-paul-defense-spending/