He's not talking about the Constitution.
The sad fact of the matter is that the original British settlers who colonized what was later to become the United States were Christians. Intolerantly so, which was the main reason they did not stick around Britain in the first place. While many of the Founding Fathers were themselves deists and perhaps atheists, a great many of the average people living here were Christians. For better or, more likely, for worse, the mainstream culture developed out of Protestant Christianity. Nations do not develop in a vacuum, but rather around prevailing mores and principles.
To put it in another perspective, there was more to the founding of the United States of America than simply the Revolution or the Constitution. Nations aren't formed by documents, after all, but rather by people. The people that form a nation are not just that nation's leaders, but also the ordinary populace. The beliefs and principles of that ordinary populace have an enormous effect on the shaping of a nation's character.
Lest what I am saying be misconstrued, however, I will now point out that I only defend the notion that this country was very much founded on Christian principles so that I might point out that it is probably the biggest reason as to why this country is so messed up. Christianity is such an ingrained part of this country's culture that we are having great difficulties taking part in the 21st Century. Post-Christian societies throughout Europe have moved onto bigger and better things under the realization that governments really can serve the fundamental needs of their people. Meanwhile, back in the US, we have an underlying culture that fears all government as the tool of "the Antichrist", which is the primary reason as to why conservatives and fundamentalist Christians are so strongly anti-government.
So yes. Culturally speaking, the United States of America is founded upon Christian principles. Conservatives most definitely expend considerable effort pointing this out. It is not something to brag about, however, but rather something of which we, as Americans, ought to be dreadfully ashamed. Sure, our founding fathers had the foresight to try to nip this fact in the bud by ensuring that our government was in no way founded around Christianity and kept it at as great a distance as possible, but in recent years we've seen how that is becoming increasingly difficult.
