It didn't fizzle at all, but it didn't get the reaction at all that it expected. (I was born and raised in NH, and know some of the established political players personally, so I have some sense of the story.)
Basically, what happened was that the libertarians moved into NH, settled in the lovely towns that are all over the state, ran some candidates for the state House, won (not too hard - because there are 400 House seats for 1 million residence, that works out to about 1200 votes per winning candidate), and their leaders went to Concord ready to do battle for libertarian ideals.
If their image of politics was shaped by what was going on in Washington DC, they were in for a surprise, because the reaction of the other legislators (majority Democrat at the time) was along the lines of "Hi, nice to meet you! We're looking forward to what ideas you might have about how to make the state better. If you need any assistance working with the various offices in the state, please let us know."
What some of the Free Staters hadn't realized before that moment is that in New Hampshire the political culture focuses more on effective and good government than on party affiliation. As an example or this in action, the Secretary of State Bill Gardner (a Democrat) was appointed in 1976 by the then-Republican leaning legislature and Republican governor, and has been consistently re-appointed by both Democrats and Republicans ever since because everyone recognizes that he's both very good at doing the work and fair to everyone. It probably also makes a big difference that there are about 10 full-time politicians in the entire state (governor, 2 senators, 2 federal congresspeople, and a few city mayors), and holding any other office is essentially a volunteer role.
Well, I assumed it fizzled in the sense that nowhere near the number of people signed up for it as they expected. NH politics aren't bad, but when I lived in the neighborhood, southern NH was being invaded by Boston workers looking for cheaper digs. Granted, I haven't been there for a long time, but I had the impression that things were going in the wrong (read "progressive") political direction.