Within the USA, there has always been a relatively strong libertarian voice, in contrast to most other countries. And within the libertarian movement, two strands have quarreled in a civil but not altogether gentle tone.
I have in mind the argument between those who believe in limited government'-usually called minarchists'-versus those who want no government at all'-called anarchists. (This last, however, does not, akin to classical anarchists, reject all laws and their enforcement.)
Before discussing these two positions, it will help to place libertarianism in perspective. Throughout human intellectual history, there have always been a few voices raised against statism, the belief that in human communities sovereignty rests with the government. This is embraced in monarchy, socialism, fascism, communism, and theocracies. Government is seen either as God-on-earth or the-will-of-the-people (as a whole). In all these statist outlooks, the individual members of society are taken to be subservient, lowly beings, or simply cells in the body of the society, which is the locus of value.
Now and then, statist views have been challenged, but since power has been concentrated in the state, they rarely got sufficient airing. When government owns the presses, forums of discussion such as universities, or parks where speeches may be given, it is no wonder those who support one or another version of the powerful state stand in the limelight, with the few opposite voices basically marginalized if not killed off outright.
After a while, though, governments proved to be so corrupt, so unruly, and so capricious that too many folks began to see it as a threat and the ruse that it is. The lie that it's God's representative on earth or it expresses the will of the people just could not be made believable enough to suppress all the opposition. The power of monarchs-'tsars, pharaohs, and such'-began to be questioned and in time contained. The idea that royals aren't anything special, after all'-that all the self-important ministers and their favored nobility were just pretending to be endowed with special rights (divine rights, it used to be called)'-began to catch on.
Eventually, certain thinkers who studied these heretical thoughts developed solid arguments and got published somehow, and the notion of the sovereignty of human individuals, as opposed to states, became palatable enough to inspire influential and clever people to translate them into law and public policy. The American Founders were the most successful of these people, managing to declare to the world that it is individual human beings who have unalienable rights to their lives, to their liberties and to the pursuit of their happiness. However much or little they succeeded in curtailing the powers of the state, the idea that this may well be a good idea could no longer be kept out of circulation.
Unfortunately, bad habits are difficult to shed, so the actual legal order they forged didn't fully recognize and protect unalienable individual human rights. And many elements of the old system were kept intact, such as taxation, conscription, secondary citizenship for various groups, and even slavery. But the cat was out of the bag, intellectually--as Abe Lincoln somewhat duplicitously put it, 'No man is good enough to govern another man without that other's consent.'
The result was the eventual development of the libertarian alternative to all varieties of statism. This development, however, didn't resolve one of the questions that has always been on the minds of political thinkers, namely, whether government of any type is evil, a criminal organization disguised as something necessary for society, or the germ of legitimacy to the institution, only it has been twisted by power hungry rulers and their apologists to serve corrupt ends.
Libertarians, unlike old line anarchist, recognize the value of law and even law enforcement. What some of them argued is that any law enforcement agency must itself be deprived of its monopoly status, be competitive, so it is subject to a repeated cleansing process. Just like other things people want or need, law, too, must be possible to be offered by many agents who can provide it.
Those libertarians who think government has merit, provided it is kept within proper bounds, disagree with this, but only to a relatively minor degree. They think that in some ways law enforcement will always be monopolistic, but not different from, say, how an apartment house or department store is monopolistic'-namely, only one can exist in one geographical spot. If you want to get to a competing agency, you need to move there.
Most libertarians do not see this as a deal-breaking dispute. They are mainly concerned with the central point: Who is to rule our lives? Is it to be individuals, within their own delimited sphere, wherein no one may enter who hasn't obtained permission, where no governing may occur unless consent of the governed has been given? Or is it to be some self-selected persons or groups, people who either rule others on their own initiative or who claim to speak for everyone and impose their (majority, minority) plans on all, never mind consent.
The libertarian alternative is still marginalized. This is perhaps analogous to how the idea of equal standing under the law for women is marginalized across the globe. Both of these ideas, of course, deserve a serious hearing and, as best as I can tell, ultimate success.