A very well written post on the LP over at the Volokh Conspiracy, to wit:
Some LP defenders argue that even if the Party doesn’t have any chance of winning, it can at least help educate the public about libertarian ideas. However, there is little if any evidence that the LP has actually had any success in this task over its 35 year history. Those libertarians who have succeeded in spreading libertarian ideas – people like Milton Friedman, Ayn Rand, and the Cato Institute – have done so without any LP affiliations, and indeed have tried hard to work with the two major parties. Whether fairly or not, the mainstream media and academic world are not going to pay much attention to ideas emanating from a tiny third party that has no chance of winning any elections; therefore, the LP’s educative potential is unlikely to be much greater than its electoral potential.
If we had a proportional representation electoral system, like many European countries and Israel, a separate libertarian party would make excellent strategic sense. The party (if better run than the dysfunctional LP) could command 10-15% of the vote, thereby winning roughly that percentage of legislative seats, and would be a potential part of a ruling political coalition. A libertarian party might also make sense if one of the major political parties were on the brink of collapses and the libertarian party stood a chance of taking its place (as the Republican Party displaced the Whig Party in the 1850s). However, in the real world, the US is unlikely to move toward proportional representation and neither major political party is likely to collapse anytime soon. Therefore, the cause of libertarianism will be better off without a separate Libertarian Party.