Technically, "the idea that government intervention is morally wrong" when combined with "in every case" is anarchism, obviously.
Most libertarians (big and little L) believe the government does have a few legitimate roles, often including national defense (and not offense) and defense of basic human rights (via police and a court system). Libertarians are an extremely argumentative bunch, and you'll be hard pressed to find two who believe the exact same things. Keeping a libertarian "on message" would be an exercise in frustration...which I guess is one reason why none ever get elected.
I'm a card-carrying member of the LP, though ethically, the purity of anarchism is appealing to me. Regardless, I'd be perfectly content, and would feel very much less disenfranchised and poorly represented, with a government that looked a lot like the one originally envisioned by our founding fathers, which is, I guess, "Republican" in the traditional sense.
Just to clarify, there is a simple general principle at work: the government should provide only public goods (1). The main dispute among libertarians is which goods qualify as public goods (e.g., is fire protection public or private?).
(1) A public good is one that is non-rivalrous and non-exclusive. Protection from commies is a public good (a dead commie isn't robbing you or me). Cheese fries are not (every fry I eat is one you can't).
In every case? Does this make logical sense? How can this be justified for all possible conditions and outcomes?