Going against social security and medicare is political suicide, and a libertarian who supports those programs, well, that's pretty much a LINO (trademarked!) and the GOP is already filled with those.
Yeah, I don't see it. There aren't very many actual libertarians out there. Republicans are happy to use libertarian language on taxes and spending, but this is just cover for wanting to cut
other people's government benefits. And that kind of hostility to the Other goes hand-in-hand with social conservatism. The natural compromise party seems to me to be populist/anti-libertarian. Look at right-wing parties in Europe.
There's enough of a libertarian presence in the Republican party that it wouldn't shock me if someone like Ron Paul were to win a primary at some point because of his fans' enthusiasm, but I think such a candidate would lose the general, and badly.