"However since about 85% of the Constitution is English Common Law the traditions you speak of were certainly inherent."
The founders didn't say the ten commandments were inherent as some long gone influence that they would grudgingly have to tolerate as a religious influence from history. They said that the very foundation of the Constitution IS directly based on Christianity and the ten commandments.
There is no mention of a secular basis in the Constitution, so according to your logic that must prove that it is based on God.
All 50 constitutions mention God as the source. Tell me which of the founding fathers (see below) changed the foundation of the Constitution from God, Christianity and the ten commandments to pure secularism completely void of God all of a sudden when it came to the US Constitution?
Joseph Story is THE man to nail this down: "There never has been a period in which the Common Law did not recognize Christianity as lying its foundations."
Need I say more? Let's hear from a few more important founders...
Thomas Jefferson said, in 1781 just after the Massachusetts constitution was ratified: "God who gave us life gave us liberty. And can the liberties of a nation be thought secure when we have removed their only firm basis, a conviction in the minds of the people that these liberties are the Gift of God? That they are not to be violated but with His wrath? Indeed, I tremble for my country when I reflect that God is just; that His justice cannot sleep forever.?" -- Notes on the State of Virginia, Query XVIII, 1781, p. 237
James Madison: "I have sometimes thought there could not be a stronger testimony in favor of religion or against temporal enjoyments, even the most rational and manly, than for men who occupy the most honorable and gainful departments [of government] and are rising in reputation and wealth, publicly to declare their unsatisfactoriness by becoming fervent advocates in the cause of Christ; and I wish you may give in your evidence in this way." -- Letter of Madison to William Bradford (September 25, 1773), in 1 James Madison, The Papers of James Madison 66 (William T. Hutchinson ed., Illinois: University of Chicago Press 1962).
George Washington: "... forbid us to expect that national morality can prevail in exclusion of religious principle. It is substantially true, that virtue or morality is a necessary spring of popular government. The rule, indeed, extends with more or less force to every species of free government. Who, that is a sincere friend to it, can look with indifference upon attempts to shake the foundation of the fabric? -- Address of George Washington, President of the United States . . . Preparatory to His Declination (Baltimore: George and Henry S. Keatinge), pp. 22-23. In his Farewell Address to the United States in 1796
Benjamin Rush (Signer of the Declaration of Independence): "...the only means of establishing and perpetuating our republican forms of government, that is, the universal education of our youth in the principles of Christianity by the means of the Bible. For this Divine Book, above all others, favors that equality among mankind, that respect for just laws, and those sober and frugal virtues, which constitute the soul of republicanism. -- Essays, Literary, Moral and Philosophical (Philadelphia: Printed by Thomas and William Bradford, 1806), pp. 93-94.
Th Jefferson: "I reciprocate your kind prayers for the protection & blessing of the common father and creator of man [God], and tender you for yourselves & your religious association, assurances of my high respect & esteem." -- Jan. 1. 1802.
Thomas Jefferson: "The doctrines of Jesus are simple, and tend all to the happiness of mankind." -- The Writings of Thomas Jefferson, Albert Bergh, editor (Washington, D. C.: Thomas Jefferson Memorial Assoc., 1904), Vol. XV, p. 383.
See: http://www.wall-of-separation.com