The problem is that it is not supported by anybody except for the rare libertarian thinkers. Here’s my (very inaccurate) demonstration of common types of mindsets showing why it is so.
Entrepreneurs by the very definition of their job have to deal with whatever situation is at hand and not waste time discussing political philosophy. They need to get the job done within an existing framework, whether it is a monarchy, democracy or socialism. Theory of justice is not a good guidance, especially if it goes against the existing rules. Entrepreneur tends to be efficient first, moral second. Otherwise the more efficient one will take his place. Entrepreneur’s perspective is solely from his own enterprise and its profitability. If it is not so, there will quickly come another one, more focused and more efficient to win the customers.
Politicians by definition oppose libertarianism. Politicians fight for power, their piece of the pie. While the entrepreneur tries to maneuver within the existing rules as efficiently as possible in order to create his product, the politician is interested in changing or creating rules according to his own ideas of what’s good and bad. (Sure enough, a single person may combine both roles, but it is useful to analyze them separately).
Regular wage earners do not fight for power like politicians, nor do they build their enterprises and products. They focus on their own work and life and prefer a stable income. Those of them who are interested in any social philosophy are not going to like libertarianism very much for it does not promise them anything in particular. Every politician, left or right, promises safety, stable prices and free stuff, but only a libertarian will promise you that you are going to earn what you deserve, no less, no more.
Who remains then? Those people who are not starving, who have the time and cultural background to study things, who have no desire or skills to fight for power or bring about a particular enterprise, are in a most favorable position to start learning libertarianism. And still many of them would not be convinced at least for the reasons outlined above.
Here are the implications of this realization. First of all, there is no threat (or hope) that the libertarian movement will suddenly make a big impact. Then, those who have any interest in libertarianism have to admit that they will not attract many supporters due to the very nature of the theory. When people say that libertarians “define their reality in their own head” it is a sign that they are not interested a priori. There is little hope that people will “get interested” if you repeat your idea over and over again. This just pisses them off. Look at the people around you: everybody is interested in their own benefits (material or psychic).
A socialist who promises a particular policy and particular effects based on carefully chosen historical data points is by far more efficient in convincing a random person than a libertarian who carefully analyzes the nature of all human actions and then comes up with something vague and unimpressive like “everybody will be able to freely pursuit their own happiness”. To believe a socialist you just need to be convinced by some data points and concrete goals. But to believe a libertarian you need to study all that stuff yourself because on the surface it looks either “crazy” or “simplistic”. Not many people have the time and energy to even try.