Democrats attract young people too with it's pie-in-the-sky ideology, unworkable economic theories and promises of free stuff.
The Libertarian is the largest third party, but it's a long, long drop after the #2 Republicans. Of course it has too many idealists and wackadoodles.
Here's the key thing most political partisans forget: it's natural for human beings to lean towards idealism or realism, towards liberalism or conservatism. "Leaning" doesn't mean go fullblown nutjob as we often see on political forums. Most people are somewhere in between the extremes.
That said, regardless what you call it, and with our current level of tech, it's natural that one party would lean Left and the other Right. Countries with Parliaments have similar splits, just more of them. The whole House of Lords and House of Commons is a split between conservatives and liberals, between those with the money and those who work for money.
Getting rid of the these systems is impossible without replacing our need for a finite supply of resources. Due to current events, at most you can expect to see the Democrats dominate for the next 2-3 elections.
After that it depends upon whether they fuck it up or not. I have faith in human nature meaning, oh yes, they'll fuck it up.