The Constitution mainly derived from British commonlaw, the Magna Carta, the British Bill of Rights, other constitutions abroad, state constitutions, and Enlightenment era philosophy.
The Due Process Clause of the Constitution was partly based on common law and on Magna Carta (1215), which had become a foundation of English liberty against arbitrary power wielded by a ruler.
British political philosopher John Locke following the Glorious Revolution (1688) was a major influence expanding on the contract theory of government advanced by Thomas Hobbes. Locke advanced the principle of consent of the governed in his Two Treatises of Government. Government's duty under a social contract among the sovereign people was to serve the people by protecting their rights. These basic rights were life, liberty and property.
In his The Spirit of the Laws, Montesquieu argues that the separation of state powers should be by its service to the people's liberty: legislative, executive and judicial.
The constitution was a federal one, and was influenced by the study of other federations, both ancient and extant.
The English Bill of Rights (1689) was an inspiration for the American Bill of Rights. Both require jury trials, contain a right to keep and bear arms, prohibit excessive bail and forbid "cruel and unusual punishments". Many liberties protected by state constitutions and the Virginia Declaration of Rights were incorporated into the Bill of Rights.
I think references to Judaism and Christianity in the Constitution are virtually nonexistent, aside from the word "blessings," in the preamble, which does not evoke any particular religion. There are no references to Jesus, Moses, Yahweh, the Bible, the Torah, or the Ten Commandments. The ideologies of the Constitution do not seem to line-up very closely with the ideologies of the Bible; aside from that the Constitution and the New Testament both promote general welfare. The Constitution enumerates some of the peoples' rights that the federal government should not infringe upon. The Bible / Torah does not do that at all; the closest thing it does is hand down laws of God, many of which do not line-up with the U.S.'s legal system.
So I would contend that the Constitution is more of a document of Enlightenment thinking than it is a Judeo-Christian document. It's been influenced by William Blackstone, John Locke, Montesquieu, Edward Coke, Thomas Hobbes, Francis Bacon, John Milton, William Penn; and of course, Enlightenment-era Americans like John Otis, Benjamin Franklin, Patrick Henry, and Sam Adams.