The biggest problem for an individualistic, freedom-oriented political movement is getting each of those individuals to join any sort of movement in the first place.
Many economists wonder why anyone votes at all -- the chance of any one ballot changing the outcome is statistically zero and the cost of voting is small but positive (e.g. risk of dying in a car accident on the way to the polls), so rationally it would be better to stay home on election day. Most people vote out of a feeling of moral obligation or civic duty.
The low impact of voting helps to explain why barely more than half of the American electorate usually shows up to vote. That problem is magnified for a political party whose "base" has a strong individualist leaning; they are less likely to feel the civic obligation which pushes others to the polls.
Enter the Free State Project. Goal: collect signatures from libertarians, who will move to New Hampshire when total signatures reach 20,000. Why New Hampshire? It has low tax rates, little dependence on federal spending, and a small enough electorate that 20,000 people might be able to sway its political orientation.
In economic jargon, the Free State Project uses a pre-commitment device to solve a collective action problem. No one is asked to move to New Hampshire until sufficient signatures are obtained (as of this writing there are 11,578 participants; 8,422 to go). Any one person moving to New Hampshire in order to change its politics would bear a large cost, with uncertain chance of success. Assuming people stick to their word, the Free State Project allows each person more confidence that their action will make a difference.
Agree or disagree with the libertarian political platform, it's hard to argue about because there are few real examples of libertarian societies to reference. I hope the libertarians do succeed in taking over New Hampshire, because it will be an interesting test case for a liberty-motivated legislative majority. Even if the result is a total disaster the impact will be negligible, and the advance in knowledge for political science / public choice well worth it.