The Libertarian Party has grown significantly since their creation in the 1970s. The Libertarians even steal votes in local elections away from Republicans often. The best example would be the last Governor election in Virginia. The Republican Party will convert to more Libertarian ideals or they will be replaced in many districts. The Libertarians are mad at the "statists," and their message is spreading like wildfire. The Republican Party will not be able to stop the inevitable.
They are way too radical. Most people no longer care about what a person does in the bedroom. Most people no longer support a party that goes "nation building" and blowing a tons of money on a junk jet. Most republicans act like they are Hitler and expect you to be a good Christian
Most conservatives have libertarian values on fiscal issues. Many liberals have libertarian values on social issues. So why hasn't the libertarian party seen success? The answer is that most conservatives won't support a party that wants drug legalization and gay marriage. Most liberals won't support a party that believes in free-market capitalism. The idea that the libertarian party will replace the Republican party relies on 2 false assertions: 1-Social conservatism will disappear. 2-The Republican party will be unable to sell its message to the people. If these were true, then another party would emerge to challenge the liberal Democrats. The Republican party will slowly change its stance on issues where most people disagree with them, and the party will remain viable. The so called "far-right" will support the GOP as the lesser of 2 evils (because forming their own party would guarantee Democrat supremacy).
The Libertarians have been trying forever to get government down and big business up. They have failed every step of the way. The problem with libertarians is that seem to think they're above the "left-right" arguing, but they're just a group of extremist who think government is a bunch of demons and big business is a gift from god. The American people don't like government, sure, but get rid of it like the LP suggests, never, 50% of the country would not vote for a libertarian over a republican
Although they support many of the same ideals, the Libertarian party will never replace the Republican party because 1.) the Republican party has too much power, and 2.) the existence of the two-house system. Nevertheless, I firmly believe that one day the two-house system will collapse, and when it does, it will be the success of other independent parties. Including, but not limited to, the Libertarian Party, the Socialist Party and the Green Party.
Party line Republicans wish to limit the government, Libertarians want to gut it completely and for it to have almost no power. Those biews might sound similar, but in the end are completely different. Also, the Republican party isn't about to be phased out. The GOP owns the House, and holds a majority of the Governorships. They aren't going amywhere for the time being.