That whole "truths to be self-evident" thing...
Natural law is certainly a concept the Angelican Church retained after it split from Rome. But I think perhaps you should review a couple of pieces before deciding the Founders were these great theistic philosphers:
A Catholic Response to Certain Myths of Civic Americanism (1997) Is the individual all-important? Is civil society an invention of human convenience? Are all men created equal? Is freedom the great political objective, and tyranny the thing to be feared most in life? Is religious liberty really a good idea? Is America a Christian nation? Was the French Revolution that different from our own? We answer these and other questions in a way you’ve perhaps never seen before. More importantly, we trust that we answer them correctly.
http://www.charlesdenunzio.com/myths.html
Which is actually just a chapter from the larger work:
Variations on a Theme, Op. 45 (1998) The situation of the Catholic Church in the United States we see today is a product of not only these last forty years, but rather has its genesis in the attitudes of English and American churchmen predating even Archbishop John Carroll — attitudes that permitted American Catholics to uncritically accept a cultural outlook that in theory always was, and now in practice has shown itself to be, vitiating and even destructive of their Faith. [The link leads to the main portal page for this manuscript, which was the eventual result of The Catholic Church & American Culture Project, the endeavor that inspired the very existence of this journal itself.
http://www.charlesdenunzio.com/op45/
The philsophical underpinings of the Constitution and Declaration are more in keeping with the dominant Protestant and Deist thought of the time, connected by the work of Hobbes and Locke.
Living under the Leviathan [Matthew M. Anger, 2002]: The extreme individualism of Hobbes and Locke (undergirding classical civic Americanism) has given way to the extreme egalitarianism of Rousseau (exemplified in Political Correctness), and no wonder: both strains of thought have crucial fundamentals in common. [Replaces “The Legacy of Hobbes and Locke,” posted here in 1996.]
http://www.charlesdenunzio.com/hobbes.html
This is what's missing, I think, in the discussions of why does our society keep sliding towards more and more collectivist organizations. It's also key to understanding moral relativism, which is of course the antithesis of natural law theory.
Understanding that the roots of Marx lie in the work of Locke, Hobbes and Protestantism is crucial. American "conservatives" that tout a return to the "vision of the founders" miss the whole point that what we have now is a natural outgrowth of their vision.
A key modern document of the Church, in refutation of relativism and affirmation of the natural law is Veritatis Splendor (The Splendor of Truth - Regarding Certain Fundamental Question of the Church's Moral Teaching) August 6, 1993
You can find it here:
http://www.vatican.va/holy_father/john_paul_ii/encyclicals/documents/hf_jp-ii_enc_06081993_veritatis-splendor_en.html
This is an extensive document that the scholar should study at length, I'll only quote the stated purpose given for it's promulgation by John Paul II:
The purpose of the present Encyclical
4. At all times, but particularly in the last two centuries, the Popes, whether individually or together with the College of Bishops, have developed and proposed a moral teaching regarding the many different spheres of human life. In Christ's name and with his authority they have exhorted, passed judgment and explained. In their efforts on behalf of humanity, in fidelity to their mission, they have confirmed, supported and consoled. With the guarantee of assistance from the Spirit of truth they have contributed to a better understanding of moral demands in the areas of human sexuality, the family, and social, economic and political life. In the tradition of the Church and in the history of humanity, their teaching represents a constant deepening of knowledge with regard to morality.8
Today, however, it seems necessary to reflect on the whole of the Church's moral teaching, with the precise goal of recalling certain fundamental truths of Catholic doctrine which, in the present circumstances, risk being distorted or denied. In fact, a new situation has come about within the Christian community itself, which has experienced the spread of numerous doubts and objections of a human and psychological, social and cultural, religious and even properly theological nature, with regard to the Church's moral teachings. It is no longer a matter of limited and occasional dissent, but of an overall and systematic calling into question of traditional moral doctrine, on the basis of certain anthropological and ethical presuppositions. At the root of these presuppositions is the more or less obvious influence of currents of thought which end by detaching human freedom from its essential and constitutive relationship to truth. Thus the traditional doctrine regarding the natural law, and the universality and the permanent validity of its precepts, is rejected; certain of the Church's moral teachings are found simply unacceptable; and the Magisterium itself is considered capable of intervening in matters of morality only in order to "exhort consciences" and to "propose values", in the light of which each individual will independently make his or her decisions and life choices.
We essentially find ourselves in an age where many, perhaps even the majority, take the position of Pontious Pilate when he cynically asks Christ "What is truth?"
The state of Nature has a law of Nature to govern it, which obliges every one, and reason, which is that law, teaches all mankind who will but consult it, that being all equal and independent, no one ought to harm another in his life, health, liberty or possessions; for men being all the workmanship of one omnipotent and infinitely wise Maker; all the servants of one sovereign Master, sent into the world by His order and about his business; they are His property, whose workmanship they are made to last during His, not one another's pleasure. And, being furnished with like faculties, sharing all in one community of Nature, there cannot be supposed any such subordination among us that may authorise us to destroy one another, as if we were made for one another's uses, as the inferior ranks of creatures are for ours. Every one as he is bound to preserve himself, and not to quit his station wilfully, so by the like reason, when his own preservation comes not in competition, ought he as much as he can to preserve the rest of mankind, and not unless it be to do justice on an offender, take away or impair the life, or what tends to the preservation of the life, the liberty, health, limb, or goods of another. (Two Treatises on Civil Government)