David Brooks raises the interesting issue of why, given the basic popularity of many large-scale liberal initiatives, does America have so few self-described "liberals" in it. In lieu of discussing this issue in terms of survey data or sociological research, Brooks prefers to posit that many Americans shy away from liberalism for complicated public choice reasons that sound an awful lot like David Brooks' personal critique of liberalism rather than David Brooks' theory of the structure of American opinion.
I don't actually think Brooks is confused about the difference between the two. But I think it's a somewhat interesting issue. One of the most relevant pieces of survey data on this that I've seen recently was a December Pew survey reproduced to the left, which showed that while people have a fairly negative reaction to the term "liberal" they're enthusiastic about the term "progressive." I think it bears noting that "progressive" is the word most mainstream center-left institutions have chosen to define themselves. At any rate, any theory about the deep structure of American opinion should be robust to the change in wording. All the reasons Brooks gives to not be a liberal apply equally to progressive. Another relevant datapoint from the biannual American National Election Survey is that typically liberal self-identification is more popular among whites than among African-Americans. This is a curious fact, since just about every other measure we have indicates that left-wing political views are more common among African-Americans than among whites.
I personally share Brooks' concern that there's too much rent-seeking in the American state, and that too many programs are unduly geared toward the interests of service providers rather than people in need (the recent dustup over LIHEAP is a case in point). But I don't think this concern has much explanatory power in terms of the structure of American opinion.