Ed Darrell is a Constitutional lawyer who wrote this about God in the Constitution, in reply to someone who asserted there is no separation of church and state in the Constitution:
Separation of church and state: Its in the Constitution. I dont play a constitutional lawyer on television, I am one*, but it seems to me anyone can read the Constitution and see. Especially if one understands that the Constitution sets up a limited government, that is as Madison described, one that can do only what is delegated to it. The Constitution is a short document.
First, in the Preamble, it is made clear that the document is a compact between citizens: We the people . . . do ordain and establish this Constitution . . . The usual role of God ordaining (in some western nations) is altered, intentionally. It is not God who establishes this government, but you and I, together. From the first words of the Constitution, there is separation of church and state.
Second, in Article 1, the legislative branch is given no role in religion; neither is any religion given any role in the legislature. In Article 2, the executive branch gets no role in religion, and religion gets no role in the executive branch. In Article 3, the judicial branch gets no role in religion, and religion gets no role in the judicial branch. In Article 4, the people get a guarantee of a republican form of government in the states, but the states get no role in religion, and religion gets no role in state government. This is, by design, a perfect separation of church and state.
Third, in Article VI, the hard and fast rule that no religious test can be used for any office in government, federal, state or local, means that no official will have a formal, governmental role in religion, and no religion can insist on a role in any officials duties.
Fourth, Amendment 1 closes the door to weasling around it: Congress is prohibited from even considering any legislation that might grant a new bureaucracy or a new power to get around the other bans on state and church marriage, plus the peoples rights in religion are enumerated.
Fifth: In 1801 the Baptists (!) in Danbury, Connecticut, grew concerned that Connecticut would act to infringe on their church services, or teachings, or right to exist. So they wrote to President Jefferson. Jefferson responded with an official declaration of government policy on what the First Amendment and Constitution mean in such cases. Jefferson carefully constructed the form of the device as well as the content with his Attorney General, Levi Lincoln, to be sure that it would state what the law was. This letter is the proclamation. Its an official statement of the U.S. government, collected in the presidents official papers and not in his personal papers. Make no mistake: Jeffersons letter to the Danbury Baptists was an official act, an official statement of the law of the United States. Jefferson intended it to assuage the Baptists in Danbury, to inform and warn the Connecticut legislatures, and to be a touchstone to which future Americans could turn for information. It was only fitting and proper for the Supreme Court to use the letter in this capacity as it has done several times.
Sixth: The phrase, separation of church and state dates back another 100 years and more, to the founding of Rhode Island. It is the religion/state facet of the idea of government by consent of the governed without interference from religious entities, expressed so well in the Mayflower Compact, in the first paragraphs of the Declaration of Independence, and carried through in the Constitution (see especially the Preamble, above).
No, the phrase separation of church and state never appears in the Constitution. The principles are part of the warp and woof, and history, of the document, however. The law is clear, was clear, and denying the Constitution says what it says wont change it or make it go away.