Ed Brayton has a great post where he cites an essay of Harry Jaffa's entitled, "The False Prophets of American Conservatism." Scrolling down the comments you will see that John Coleman made a thoughtful post as did I.
Especially important is Jaffa's explanation of how the theory of natural right that founds this nation deals with religion and government. I often assert that the natural law of the Declaration holds X, and then I might quote from Madison's Memorial and Remonstrance, or Jefferson's Virginia Statute on Religious Freedom. What many don't understand is that those two documents are part & parcel of the same natural law/natural rights theory (the organic law of the US and of all liberal democracies) as the Declaration. They are practically extensions of that document.
As Jaffa notes:
The Constitution of 1787 heralded the novus ordo seclorum, the new order of the ages, when it declared that there should never be a religious test for office.
There was no precedent for this in human history. The subsequent provision in the first amendment, against an establishment of religion, and against any prohibition of its free exercise, applied -- at least before the fourteenth amendment -- only to the federal government. But the pure doctrine, as it applied to all free government, was enunciated the year before the constitutional convention, in the statute of Virginia for religious liberty.
That statute, drafted by Thomas Jefferson, was the outcome of a long and intense struggle for disestablishment of the Episcopal Church, a struggle led by James Madison, and supported by George Washington. Madison's 1785 Memorial and Remonstrance against religious establishment is unsurpassed in the acuteness of its reflections on the relationship between religious freedom, true religion, and free government. Jefferson put these thoughts into final form in the statute, which declared that "our civil rights have no dependence on our religious opinions, any more than our opinions in physics or geometry."
While the Virginia law of 1786 applied only to Virginia, its argument became in time the basis, not only of federal law, but of the law of all fifty states. It was clear to the Founders, if not to Mr. Kristol (or to Justices Scalia and Rehnquist), that a system of majority rule was impossible if the majority had the power to decide in what way its citizens must worship God. No Catholic could be compelled by majority rule to become a Protestant, or vice versa. No Jew could be compelled by majority rule to become a Christian, or vice versa.
Only by removing all such questions of religious belief from the political process, was government by majority rule possible. Nor was this designed only to provide for civil peace. Removing both penalties against nonconformity and rewards for conformity contributed greatly to the purity of religion. A man's relationship to his Maker ought to be exempt equally from the fears and temptations of politics. As Pope John Paul declares, "the fundamental right to religious freedom is the guarantee of every other human right."
Another commenter, a legal positivist, alludes to Philip Hamburger's tome, Separation of Church and State. I finally got the book and am reading it very slowly and carefully. Right off the bat, it appears that Hamburger is a legal positivist, arguing as a matter of strict constitutional technicality and procedure, why the Jeffersonian/Madisonian ideal of separation was not how the majority understood the Establishment Clause to apply.
For instance, check out this review of Hamburger's book by Robert Bork:
James Madison's role is instructive. In his 1785 "Memorial and Remonstrance," he argued that religion and government should have nothing to do with each other. But that was not the position he took in his drafting of the First Amendment. As Hamburger explains, "Madison reconciled himself to language less sweeping than that he had used in 1785, and Congress adopted a moderated version of the no-cognizance standard, which did not forbid all legislation respecting religion."
It's true that Madison attempted to use broader language in the First Amendment, language that would apply to state governments as well as to the Federal government, but had to settle or "compromise" for "Congress shall make no law respecting an establishment of religion...." But the Constitution, indeed that provision as well as many others, was written in broad generalities, thus leaving a lot of "gaps" to fill when deciding specific cases & controversies and formulating specific doctrines. I think it's reasonable to argue that the theory of natural right (the one found in the Remonstance and Jefferson's statute) could be used to fill those gaps and otherwise give meaning to the Constitution.
And there is evidence that Madison himself imputed these natural rights ideals into the Constitution, regardless of the "compromises" on the exact language that had to be made. For instance, in his Detached Memoranda, Madison asserted that the appointment of Chaplains to the two Houses of Congress was "a palpable violation of equal rights, as well as of Constitutional principles." Indeed, in that document Madison seems argue that the Constitution demands "that religion and government should have nothing to do with each other" just like he argued in his Remonstrance.
If you read the Constitution unmoored from its natural rights ideals, then Philip Hamburger is probably right. But if you read the Constitution through the lens of the Declaration and the theory of natural right that founds this nation, with its sweeping ideals of liberty and equality, especially liberty and equality of conscience, then Hamburger is wrong and we should look to the Memorial and Remonstrance and Virginia Statute on Religious Freedom to determine what degree of separating Church and State is necessary to respect the natural rights of individual citizens of the nation.