Here is how he sums it up:
The God of the Declaration of Independence is not only the author of natural rights and the judge of the world, but He also governs the world by His "Providence." The term "providence," as it was used in the eighteenth-century, was usually used to describe an active God who sustains the world through His sovereign power. This is not the distant God of the deist, but a God who is always active in ordering His creation. He performs miracles and answers prayers. By referencing "Providence," the members of Congress were affirming their belief that God would watch over them and protect them in this time of uncertainty, trial, and war. Whether they embraced all of the tenets of orthodox Christianity or not, most of the signers could affirm a belief in the providence of God.
In the end, some may be disappointed with the way in which Jefferson, his committee, and the Second Continental Congress did not produce a Declaration of Independence that was overtly Christian. The Declaration never mentions Jesus Christ, does not quote the New Testament, and fails to move beyond vague descriptions of God.
While we would be hard pressed to describe the Declaration as a uniquely “Christian” document, it certainly does reflects the theistic world view prevalent in the eighteenth-century British-American colonies.
Read the rest of the post for his analysis of the four times the DOI invokes God.