That's a great idea and in an idealistically pure country it would work. but realistically even if the libertarian party got 20% of the vote the republicrats and demicans would just unify on all things freedom and security related. So what you are talking about is a party, coming out of nowhere, getting at least 51% of the vote for the president and in both houses of congress. Even then the judicial branch will be against you until enough judges die off to be replaced. If you think 51% care enough about freedom from warentless searches in ANY COUNTRY you are super idealistic. Most people have been conditioned to trade freedom for "security" the median and out political system encourage it. It has nothing to do with the people who realize how evil our government is acting but everything to do with all the less than intelligent people who couldn't care less.
That's the issue we're facing. People still want to play the game, and when they realize they can't win, they don't stop playing the game, they just fold their arms and huff and say, "Well, we can't win, so why bother trying?"
So anyway, those who are winning at the game are also in control of public education, so it's taught that if you don't play the game, you're some kind of freak, an anarchist, and a terrorist, probably communist, and likely a witch. Get them while they're young and they're much more likely to stick with you forever; just look at how successful those religious have been at this. We still have grown men who believe in fairy tales; it's all they know. Same goes for government; if you don't know the alternative, you can't solve the problem, or even be aware of what the problem is, you only ever see the ragged ends of the problem's tentacles but never see the core of the problem, so you try to change things within the game but you never really solve a problem, you only improve your own condition and make it worse for someone else.
The point isn't to get a Libertarian into office. The point is to help society understand why the game of state and politics only works against them. Understanding the difference is what separates the men from the sheep, as is common to say nowadays; people must learn to educate themselves, which is exactly what is avoided in public school, and exactly what we push on the Internet. I have little hope for the generations before the dawn of the Internet, but high hopes for those who've spent most of their lives with it. Luckily, people don't live forever.