The explanation for this would be threefold. (1) Christian Democracy is a Catholic doctrine; (2) the intellectual Christian right in America is now predominantly Catholic; (3) Huckabee’s evangelicalism is communitarian and statist but anti-intellectual and nationalist.
Well, I dunno. This Wikipedia article acknowledges the roots of Christian Democracy in Catholic social thought, but goes on to note that "conservative" Protestants across Europe have also embraced the label. Yes, evangelicals are famous for being anti-intellectual, but some have noted the outdatedness of that generalization. While Huckabee’s "natural" supporters are probably more likely to be found in Walmarts than in the evangelical salons in Grand Rapids, Wheaton, or Waco, but I wouldn’t rule out some support even in those places. And I have no doubt but that Huckabee and his people would be very happy to have some (or some more?) heavy-hitting evangelical intellectuals on board. They also wouldn’t turn down support from thoughtful conservative Catholics, which might have been the point of the Chesterton quote.
So I’m first of all not sure I agree with Pomocon’s point and second of all not sure that, in the end, he might not be persuaded to accommodate himself somewhat to the necessities of the Republican coalition, should the nomination be within grasp. The conversation might look something like the one Jonah G. sketched here, though the Huckabee synthesis might look more like the unfulfilled aspiration of Bushism than small government purists would like. The important thing, I think, is to emphasize that the goal of government action is to enable families and communities to stand on their own feet.