America is substantively and experientially a deeply religious country, and its political discourse has always been saturated with religious rhetoric and imagery ... It is a country whose politics is experientially creedal. It doesn't incubate the kind of high Tory pragmatism that I admire in the English experience; or even the kind of atheist secularism that helped spawn socialism in other developed countries in the twentieth century. But the power of that religious presence — I call it “Christianism” and describe it at length in The Conservative Soul — is in many ways a testament to the strength of the secular constitution that resists it. In fact, I think that without the kind of secularism that Mark detects in the founding documents and Constitution, America would long since have succumbed to some version of theocracy or another.
Mark's basic point is that this is the natural and historical state for humankind. The achievement of keeping God at arm's length in the ordering structure of a polity is very, very rare. Very few countries have achieved it in the history of the world. America's genius is to have sustained it, even while fostering an intensely religious, roiling, and often apocalyptic culture. So Damon is right to worry about theology's political claims — especially in the last few years, and during various spasms of the past. But he is wrong in thinking, I believe, that this will lead to a collapse of the American system as such. It could lead to disastrous social policies, civil dissension, social conflict, and what we have come to call a "culture war." But even then, the impulse to junk the Constitution as a whole, and the ability even to amend it, is limited. In fact, it is remarkable how modest many Christian fundamentalists have been in addressing the Constitution's core secularism. Whether out of national pride or simply denial, it remains a fact that the main policy goals of Christianists in American history has been in amending the Constitution or bypassing it, rather than attacking it frontally.
I think the sheer diversity of religious belief and institutions in the U.S. would make the possibility of an American theocracy pretty remote, whatever our constitution looked like - particularly given that the number of theocracies instituted in the nation-states of the modern West as a whole is close to zero. (It's pretty close to zero for the pre-modern West, for that matter.) It’s possible to imagine a much more politically fragmented North America producing some localized theocracies, along the lines of Deseret and Puritan New England, but on a national level .. not so much.
I'm more sympathetic to the rest of Andrew's comments here, but it's precisely the aspects of American political history that he gets right - particularly the resilience of the constitutional order in spite (or because!) of the persistence of God-infused political activity - that makes his promiscuous use of scare-terms like “Christianist” so silly. The fact that religious conservatives, with the occasional exception, share the same commitment to the Constitution as liberal believers and secularists – and that much of the culture war, from abortion to school prayer to gay marriage, boils down an argument between two perfectly lucid, un-theocratic readings of said Constitution – and that if anything, the religious right tends to be more committed to upholding the actual text of the Constitution than their more secular foes – well, all of these points suggest, at the very least, that constantly slinging around terms that effectively equate James Dobson with a shari’a-happy Islamist might not be the most accurate way to analyze the intersection of religion and politics in the contemporary United States.
Also, you should definitely read Jonathan Rowe's critique of the Lilla thesis, which is helpfully linked from the Cato Unbound page. I'll try to say something more about the issues it raises later on.