Right Reason has an interesting post asking whether an absolutist ACLU style view of the Establishment Clause would forbid public displays of the Declaration of Independence -- with its references to a "Creator" -- just as it forbids public display of the Ten Commandments (in certain contexts, of course).
If the Establishment Clause were interpreted to forbid any kind of public reference to anything supernatural, then yes, the Declaration could not be displayed. However, I don't support that interpretation of the Establishment Clause, even though I call my self a "secularist" and believe in the Separation of Church & State.
It would be something perverse if the Establishment Clause were interpreted to forbid the display of the very document that gives us the political theory upon which the Establishment Clause is derived. Yes, the Declaration of Independence necessarily demands that Church & State be separated because, according to its theory, all men including Christians, Atheists, "Pagans and Infidels" of every sort, have unalienable free and equal rights of conscience.
We can easily contrast the Declaration with the Ten Commandments because the Declaration of Independence, NOT THE DECALOGUE, truly is the basis of our system of law & government.
Displays of the Declaration of Independence -- complete with its supernatural references -- are constitutional under the doctrine of "Ceremonial Deism." The Ten Commandments, on the other hand, are too much a reflection of "Revealed Religion" (as opposed to "Natural Religion") which our Founders wanted to drive out of politics and consign to the private sector of society.
Regarding "Ceremonial Deism," this shouldn't be understood as an endorsement of the religion of Deism, with its non-interventionist, unorthodox God, but rather a "lowest-common-denominator" God. Some "Creator," whomever He may be, one in which all monotheists may believe.
It is not at all clear that "Nature's God" is the God of the Hebrew Scriptures, or the God who gave us the Ten Commandments because many of the Founders -- although they believed in an overriding Providence -- doubted the veracity of much of Revelation, and presumably doubted that God actually Revealed the Ten Commandments to Moses.
Also, when the Founders did invoke God -- not just in the Declaration, but other important founding documents as well -- they took pains not to identify his attributes too specifically and not to identify him as the Christian, or even Judeo-Christian, God.
This is a needle that needed to be threaded: On the one hand, all men -- all sorts of heretics, dissidents, atheists and polytheists -- have equal rights of conscience. But we also needed a firm, unalterable grounding for these rights, hence, we needed to tie rights to a source beyond the control of man: God. If rights were tied to a specific Christian or Judeo-Christian God, then some might get the message that rights ONLY belong to the Judeo-Christian conscience. At least this is how Madison and Jefferson understood things.
Here is Jefferson on the connection between NOT identifying God in Christian terms, and the universal application of rights to all, including non-Christians. He is talking about his legendary VA Statute on Religious Freedom, which, like the Declaration, ties rights to God, but refuses to identify God in specific terms.
"Where the preamble declares, that coercion is a departure from the plan of the holy author of our religion, an amendment was proposed, by inserting the word 'Jesus Christ,' so that it should read, 'a departure from the plan of Jesus Christ, the holy author of our religion;' the insertion was rejected by a great majority, in proof that they meant to comprehend, within the mantle of its protection, the Jew and the Gentile, the Christian and Mahometan, the Hindoo, and Infidel of every denomination."
And here is Madison, who was essential in securing passage of the VA Statute, confirming Jefferson's account.
"In the course of the opposition to the bill in the House of Delegates, which was warm & strenuous from some of the minority, an experiment was made on the reverence entertained for the name & sactity of the Saviour, by proposing to insert the words 'Jesus Christ' after the words 'our lord' in the preamble, the object of which, would have been, to imply a restriction of the liberty defined in the Bill, to those professing his religion only. The amendment was discussed, and rejected by a vote of agst (See letter of J. M. to Mr Jefferson dated ) The opponents of the amendment having turned the feeling as well as judgment of the House agst it, by successfully contending that the better proof of reverence for that holy name wd be not to profane it by making it a topic of legisl. discussion, & particularly by making his religion the means of abridging the natural and equal rights of all men, in defiance of his own declaration that his Kingdom was not of this world."
An atheist, however, may be offended that rights are tied to any God. Or a polytheist may be offended that rights are tied to a monotheistic God. So they might argue that invoking one monotheistic God as the lowest common denominator offends their equal rights. In fact, this is exactly what Michael Newdow argued when he demanded that "Under God" be taken out of the pledge. And in doing so, Newdow was absolutely consistent with the Madisonian-Jeffersonian theory that gives his atheistic conscience no more or no less legal standing than the conscience of an evangelical Christian. It could be argued that by removing all references to God that we are in fact endorsing atheism. Newdow would reply, no, the tables would truly be turned if the words, "under NO GOD" were inserted into the pledge.
So in order to set the lowest common denominator to include atheists and polytheists, government would not be able to invoke the supernatural at all. But the problem with this, of course, is that Jefferson and Madison did, out of necessity, tie rights to God. But they also recognized that tying rights to the Christian God (I won't even say "the Judeo-Christian" God, because back in those days, Jews & Catholics were put into the same box as Deists, Pagans and Infidels), would necessarily give the impression that those outside of the Christian box didn't have equal religious rights. They threaded the needle by refusing to identify God as anything other than a generic, vague, "Nature's God."