The supreme law of the land, written in the summer of 1787, includes no references to religion -- including in the presidential oath of office -- until the conclusion of Article VI, after all that dull stuff about debts and treaties: "No religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." (There is a pro forma "Year of the Lord" reference in the date at the Constitution's conclusion.)
Original intent? "No religious Test" seems pretty clear cut.
The primacy of a secular state was solidified when the First Amendment was included in the Bill of Rights. According to Purdue history professor Frank Lambert, that "introduced the radical notion that the state had no voice concerning matters of conscience."
Beyond that, the first House of Representatives, while debating the First Amendment, specifically rejected a Senate proposal calling for the establishment of Christianity as an official religion. As Lambert concludes, "There would be no Church of the United States. Nor would America represent itself as a Christian Republic."
The actions of the first presidents, founders of the first rank, confirmed this "original intent:"
-- In 1790, President George Washington wrote to America's first synagogue, in Rhode Island, that "all possess alike liberty of conscience" and that "toleration" was an "inherent national gift," not the government's to dole out or take away
-- In 1797, with President John Adams in office, the Senate unanimously approved one of America's earliest foreign treaties, which emphatically stated (Article 11): "As the government of the United States of America is not in any sense founded on the Christian Religion, -- as it has in itself no character of enmity against the laws, religion or tranquility of Musselmen (Muslims) ..."
-- In 1802, Jefferson added his famous "wall of separation," implicit in the Constitution until he so described it (and cited in several Supreme Court decisions since).
via www.cnn.com
