Let's get a few things straight:
"Brain Dead Liberal" is in quotes. That means it's Mamet (his editors, actually, since he never even wrote that, and it was retitled) explaining to us that he no longer fits the description that fits that pejorative, in its pejorative sense only. (Meaning: There is a certain kind of follower, conformist, obedient, servile mentality associated with some, but not all, liberals, and that that mentality doesn't apply to him.) Mamet is a self-described "classical liberal" or libertarian. He has clearly stated that he can accurately describe himself with the term "liberal" only as defined by F. A. Hayek, here, in Hayek's famous "Why I am Not a Conservative," (which was an addenda to Hayek's masterpiece "The Constitution of Liberty"). Here's the link to Hayek's detailed explanation: http://www.cato.org/pubs/articles/hayek-why-i-am-not-conservative.pdf
In summary, in the United States, this makes Mamet a "libertarian," because Hayek uses the term in its full historical context, in which Thomas Paine and Adam Smith are self-described "liberals." This historical context is not taught in U.S. high-schools, (or even colleges if one doesn't master in political science or economics) because our political classes have noticed that it benefits them greatly if the masses are totally illiterate and uneducated about History, Economics, Philosophy, and Law. (These are all the subjects that Americans need to act properly as "citizens," in order to preserve the rule of law. If a public school teacher properly teaches students that the jury may disregard the law, as all of the framers of the constitution believed, then that teacher runs the risk of being attacked by the bar-licensed parents of his or her pupils, and outed as "not a team player" among other local political sociopaths. In this way, Hayek wrote, "the worst get on top" and the good are silenced.).
In Hayek's piece, he (Hayek) notes that the term "liberal" was no longer applied to Americans by the year 1910, due to the widespread hijacking of the (favorable) term by socialists in Academia. Then, as now, socialists who use the term are misusing it, but because they outnumber those who correctly use the term, the term "libertarian" has come into popular use. Both terms describe those who are "socially tolerant" and "fiscally conservative." (The term conservative is therefore rendered entirely illegitimate as a consistent statement of philosophy, because all good things about the term are encompassed in the phrase "fiscal conservatism." The remaining "social conservatism" simply means "social intolerance" or "bigotry." That being the case, there is no valid reason for intelligent and non-bigoted conservatives to continue to call themselves conservatives.)
Mamet has made himself incredibly clear on this issue, both in this piece, "Why I am No Longer a 'Brain-Dead Liberal'" and on Judge Andrew Napolitano's (now canceled) show on his"metamorphosis" on Fox News channel. (here: http://beforeitsnews.com/libertarian/2011/06/david-mamets-metamorphisis-701271.html )
He also explains in detail to John Stossel (here: https://www.youtube.com/watch?v=pIio8Jt7yLw ) that he lacks confidence in government's ability to centrally plan anything correctly. (For the record, this same idea referred to in this article was called "spontaneous order" by Hayek, but is called "emergence" by most scientists and economists of today. For a good introduction to emergence, read Kevin Kelly's "Out of Control" or Surowiecki's "The Wisdom of Crowds.")