Think about it. It's been Republicans and Democrats holding almost all the power between them since the 1850s, and the Republicans are really just a renamed wing of the Whigs. If the GOP splintered and the Tea Party split off on its own and took over most of the GOP seats, it'd be about what happened to the Whigs. Since the Republicans devoured their Whiggish host body, it's been just the two parties.
Successful third parties have popped up every so often (Free Silver, Know Nothing, Populist, Bull Moose, Reform, etc), but they did not displace either Republicans or Democrats. Some collapsed because they were single-issue or single-candidate and the moment passed (successfully or unsuccessfully).
But the inevitable fate of a successful third party in this country is not to displace one of the Big Two: it's absorption. One of the two majors will alter its platform enough to attract the base of the third party, and be thereby changed. The Democrats absorbed Populists and Socialists and became far more left-leaning and big-government in the 1920s and 1930s. There was a rumbling that Dixiecrats might split off and form their own deal in the 60s and 70s, but the GOP absorbed them and changed. And so forth. The parties might coast on their guaranteed ballot spots for decades afterwards, but they've essentially become places for failed Democrats or Republicans to go in order to at least say they were on the general election ballot. (i.e. such Libertarian values as can be mainstreamed have already been absorbed by the GOP, leaving behind the cranks and ego-cases.)
If you like a third party, it might feel good to vote for them, but you might have a better chance of seeing your goals met long term by trying to pressure Democratic or Republican candidates into adopting the values of the third party instead. (ETA: But not the Libertarians or Greens, they've been sucked dry already. You'd just be voting for a husk.)