I’m more or less a libertarian, and I voted no, the differences are too great. Yes, gun to my head, in theory a generic Republican candidate is slightly closer to libertarian philosophy than a generic Democratic one, but as I’m wont to say, that’s like choosing between a pile of crap and a pile of crap with sprinkles on it. In practice, the variation in candidates’ platfroms from the generic candidate and differences in experience and character overwhelm any potential theoretical alliance that might exist between libertarians and Republicans.
The fundamental problem, as others have pointed out, is that the whole left-right dynamic generally doesn’t fit well with most libertarians. Yes, there are some libertarians that are pro-life or whatever other things, but as a rule of thumb, most libertarians are going to be in favor of a far more limited government than most Democrats (and even most Republicans). And while Republicans are supposedly more pro free market than Democrats, most libertarians are also against a lot of the corporate well-fare and special interests that seem more common amongst Republicans than Democrats.
Yes, from a limited government perspective, the Tea Party branch of the Republicans aren’t all that far off on limited government and economic issues, the influence of the Religious Right on most Tea Party candidates makes them incompatible with libertarians on most social issues, notably gay marriage and marijuana legalization. MAYBE if the Tea Party could lighten up or at least put them as a lower priority, they might see more libertarian support. The thing is, as a general rule, libertarians can’t budge too much on that stuff since the whole point of libertarianism is limited/minimal government interference in all aspects of life, not just economic ones; it would be hypocritical to let those things slide.
But, frankly, that seems to be the largest problem with the Republican party in terms of demographics anyway: holding onto social issues that are continuing to lose support. Yes, there are some Republicans that are probably more economically inline with Democrats but find certain social issues too important to vote in favor of some particular conservative social issue, but it seems there are far more who feel the opposite, that they may actually be more economically inline with Republicans but can’t vote for a party that holds what they consider to be indefensible social positions.
Speaking for myself and some others I know, unless you’re damn near in exact agreement with me in everything else, I just cannot vote for a candidate that is openly hostile to gay rights, in favor of continuing the drug war, etc. I could potentially vote for someone who, say, finds abortion morally reprehensible in most cases, but if is not actively pursuing legislation limiting it and I believe that promise. Unfortunately, even that sort of Republican seems rare, at least around here, so I usually end up voting third party if that’s an option, or abstaining in certain votes if not.