Reasonoid-made-good Matt Welch wonders, over at an LA Times blog, what role Barry Goldwater would have had in today's GOP. He was a libertarian; the modern GOP isn't running thick with libertarians. So, no; not much of a role in the party, certainly not a presidential nomination.
That's all a jumping-off point for Welch's reasons why a "Liberaltarian" voter bloc is more or less a pipe dream.
1) There's rarely such a thing as a libertarian in local politics (where most politics are practiced), because it's awful hard to grant favors (or jobs) to either labor or business while cutting the size of government.
Tell that to Norm "Firecracker" Westwell! Still, basically true.
2) Self-described libertarians over the age of 40 who don't belong to the Libertarian Party (which is to say, most of them) are overwhelmingly likely to consider the GOP their default home, because of taxes, the memory of anti-communism, and hatred of all things McGovern/Carter (even though Carter was arguably the greatest deregulation president … though that's a rambling essay for another time).
Also true, but not the strongest argument against a growing libertarian-Democrat alliance or free-floating Democratic bloc. According to Pew, Boaz et al, there are more libertarians under 40 than over 40, and that ratio is only going to get worse for the oldsters unless Glenn Reynolds discovers the nanotech equivilent Philosopher's Stone. (He probably considers this more likely than I do.)
And in the partisan era these libertarians were born into, they watched a pork-crazed Republican Congress and a disastrous Republican presidency drastically expand the government left by sleazy but basically pragmatic Democrat—expanding it into abortion clinics, church charities, elementary schools, and of course Iraq.
3) Libertarianism just ain't that popular to begin with.
Ah, and here we go. Absolutely the full set of libertarian virtues and beliefs isn't popular, and will never achieve mass popularity. I don't think Liberaltarians (or libertarians who recently voted for Democrats, like me) expect that to fundamentally change. The way I read Lindsey's original article, I assumed we were talking about libertarians trading the battered wife status they have in the GOP with a unloved but respected wife status in the Democratic Party. We'll get a little movement on some of our issues, but more importantly we'll get swing status. Two parties that need Colorado, Nevada, Arizona, and the rest of the West to win the presidency will naturally have to consider libertarian ideas in a way they never had to when 1)libertarians were locked into the GOP coalition and 2)the West was less populous.
That might be a pipe dream, but it's a reasonably optimistic possibility that doesn't depend on libertarian ideas becoming drastically more popular than they are.