Is there a libertarian moment? The jury is still out (link).
It seems to me that most Americans hold at least a few beliefs that
could be described as libertarian. The problem is, they don't necessarily hold those beliefs due to any sort of libertarian rationale. Their libertarianism, if it exists at all, is ad hoc. They might be against drug prohibition just because they want to get high. Or they might believe in religious liberty for Christians and no one else.
In my experience, most people are inconsistent. Their beliefs are contradictory. They've never thought through the issues enough to have any kind of consistent worldview, nor do they care to. So, when I hear other libertarians say that most Americans are basically libertarian, I can't help but cringe at their naivete.
Can a fascistic neoconservative who wants to carpet bomb the Middle East be called basically libertarian because he's against minimum wage laws? Can a socialistic progressive who wants to repeal the second amendment be called basically libertarian because he's against mandatory vaccination? The answer in both cases is no.
This is setting aside the fact that many of the so-called libertarians who are talking about this supposed libertarian moment are barely libertarian themselves. I'm thinking of the sort of left-libertarians (or Beltway libertarians, or bleeding-brain libertarians, whichever pejorative you prefer) who populate the CATO Institute and other respectable "libertarian" institutions. They laud the current celebration of homosexuality as if sexual perversion actually has anything whatever to do with the political theory known as libertarianism. Rather than revealing a libertarian streak among the American populace, the recent legal enshrinement of so-called same-sex marriage actually reveals an incipient totalitarianism. At least in this instance, the left-libertarians are no different from the neocons and progressives they so loathe. Their motto is, "Liberty for me, but not for thee!"