D. Stephen Heersink leaves a comment on the topic of historical Christianity, the Bible, and Founding principles which deserves a careful read:
I don't claim to be an expert, but I am thoroughly familiar with the Bible, the Constitution, and the Declaration of Independence (and very familiar with Christian History and Theology), and I find no implicit or explicit correlation to anything in the Bible and Christian Theology/History with anything in the Founding Documents. Not a single thing. Even the single reference to a deity is by "Creator," not Yahweh, Adonai, or any other Hebrew or Christian term. I don't believe the word "Creator" is to be found in the Bible either. It's first published use was the Council of Nicea in 325. There appears to be an equivocation between "Creator" and "Maker" in different contexts, but I seriously doubt the Founders were engaged so narrowly on the distinction. Not even "Author of our Being," a popular conceptual phrase in the Bible and the early Church is not synonymous with "Creator."
Even though Athenian democracy preceded the New Testament by four centuries, the notion never appears in a biblical text. Rather, the opposite. The early Christians, from which the Bible emerged, had a very hierarchical sense of their faith, which Clement, one of the earliest Christian writers (and third successor to Peter) describes is a certain procession: "As the Father sent the Son, so the Son sent the Apostles, so the Apostles sent the Bishops, and so the Bishops send the Presbyters, who are served by the Deacons, in which the faithful believer is "overseen." The Council of Jerusalem, described in Acts 15 and elsewhere, clearly mirrors this procession, with James, the Apostle of Jerusalem presiding with his fellow Apostles. But the Apostles were not elected, indeed they cast lots (dice) in the trial by ordeal to choose Matthias to replace Judas. Subsequent bishops were not elected either, but commissioned by their predecessors, in an effort to create a historical succession of the "procession" through the "laying on of hands" transmitting Apostolic Authority through the generations. This KEY aspect of the early Church was entirely negated by the Reformation, even though it predates the Bible. In fact, its existence begat the Bible.
The notion of separate powers in balance (as in the Constitution) would have been ludicrous to the "procession" claim. Even when rulers (monarchs) wanted authority to govern, they needed the Authority of the Bishop to do so, and thus begetting the Divine Right of Kings. All authority comes from God, according to the early believers (and confirmed by scripture), so only God's Stewards of Oversight could confer Divine Authority to Rule Temporal Power.
Any sense of "rights" as we understand them today was not on anyone's radar in biblical times. Indeed, they are the invention of the Enlightenment in opposition to Authority as Christians customarily understood it. Granted, the Puritans and Protestants no longer submitted to episcopal authority, despite the biblical command to do so, but their antinomian impulses were often contrary to received traditions. But those radically individualistic impulses and a pluralistic liberal democracy achieved a sense of "inevitability" and compatibility by a new understanding of the believer as Diviner.
IF there is ANY connection, and admittedly it is tenuous, it is with the Puritan/Protestant insistence on a "direct" relationship with God (mediated through his private interpretation of the Bible) and therefore left to the "individual" to work out his salvation in fear and trembling, rather than being mediated by the "Church." This is a radical disjunction and departure from historical Christianity. The "new" sensibility is that each believer gets to divine religious truth as she sees fit, and I'll agree this independent, even anarchic, self reliant ethos played an important role in their embracing democracy, because religious truth is no longer "revealed" but "discovered," no longer "imposed," but "chosen." This independent spirit among Protestants and Englightenment thinkers was surely compatible compared to historical antecedents, but it is only this elan, not any particular religious belief or biblical sense, that linked the two disparate factors together. The ONLY connection to the Founders and the religious in the emerging nation is their joint antinomian impulses, where self-determining freedom, self-determining religious belief, and self-determining governance converged.
Those who claim the Founding Documents are "biblical" or are compatible with "Christianity must cite some example, some "correspondence," some "evidence" for their pipe dream fantasies. Clearly, the American experiment was totally at ODDS with historical Christianity (a point still relevant to Catholics as late as the 19th C), but the Self-As-Authority in Protestant religion and secular politics made a convenient bedfellow of politics and religion. In a very odd twist, if not perversity, the new breed of Christianist is not so "independent," and not so "tolerant" of others' beliefs, and in fact subscribes to principles antithetical to the 18th C. elan. Whatever the religious persuasion of each Founder, "rights" were not negotiable. Indeed, they preserved the "independent" thinking person from any religious hegemon. Yet, as we've seen recently, religious hegemony and domination, compromising rights and personal freedom, are features of the New World Order. Madison, Hamilton, Jefferson, et al. would be appalled. Angrily appalled. But even the Puritan ethic would never have embraced today's Christianist relativism toward torture. On matters of sex, Puritans were definitely inhibited, but on matter of individual liberty and divine propriety, they would never have compromised their independence for false security.