I think the Libertarian Party may well have served some useful function over the last 35 years, but at present (and in the absence of major and highly improbable changes in our electoral system) I’m inclined to endorse Bruce Bartlett’s take:
My conclusion is that for libertarian ideas to advance, the Libertarian Party must go completely out of business. It must cease to exist, period. No more candidates, no more wasted votes and no more disillusioned libertarian activists.
In place of the party, there should arise a new libertarian interest group organized like the National Rifle Association or the various pro- and anti-abortion groups. This new group, whatever it is called, would hire lobbyists, run advertisements and make political contributions to candidates supporting libertarian ideas. It will work with both major parties. It can magnify its influence by creating temporary coalitions on particular issues and being willing to work with elected officials who may hold libertarian positions on only one or a handful of issues. They need not hold libertarian views on every single issue, as the Libertarian Party now demands of those it supports.