The answer to this question is it depends. I'm going to answer Kristo Miettinen's response in a series of posts. One of Jim Babka's friends also takes issue via email on the identity of the God of the American Founding:
As for Rowe’s claim that the proclamations were made to a “generic God.” What God pray tell could they have possibly been referring to other than the God of the Bible? Now there may have been a difference of opinion about the deity of Christ, but that difference did not lead America’s leaders to a God other than the one of the Holy Scriptures.
Miettinen puts it this way:
To your claim that “the God to whom the founders appealed – the individual rights granting nature’s God – arguably was not the biblical or Christian God” I have this query: how many, among the founders, ignored the bible in seeking God? After all, even the squishy theist Jefferson was obsessed with the biblical accounts of Christ (you may be able to find the references faster than I can, but TJ was reputed to study his highly heterodox biblical compilation every night). And if you acknowledge that a biblical God was the majority (if not consensus) view, then in what sense are we not talking about a Christian God, keeping in mind as we must that Christianity in America was, then especially but largely even today, bible-based rather than creedal, and also that the bible in question was not the Tanakh or Qu’ran but the good old KJV.
My answer: Conclusions about the key Founders' view on the biblical nature of God depends on from which perspective one looks, because the glass is half full/half empty, as it were. Secularists want America's Founders to be Deists who categorically rejected Biblical Revelation and the Christian America crowd wants them Christians who accepted the Bible as infallible. But they were neither; they believed the Bible was partially inspired; parts of Scripture were legitimately revealed, parts weren't. God primarily revealed Himself through Nature, secondarily inspired the Bible, and, as Dr. Gregg Frazer put it "[r]eason was the ultimate standard for learning and evaluating truth and for determining legitimate revelation from God." So in a sense yes, this was the Biblical God, minus everything man's reason [or the key Founders' reason] deemed His irrational attributes recorded in Scripture. This is why some folks might argue, yes because they turned to the Bible [not the Koran or other holy books] for some of God's nature, it was the Biblical God, while others might note, since they edited parts of His nature from the Bible, it wasn't really the Biblical God.
In this past post on the key Founders and Scripture I noted evidence for this in the primary sources some of which I'll reproduce here. As Ben Franklin wrote to John Calder Aug. 21, 1784, he believed the Bible is not infallible:
To which I may now add, that the[re are] several Things in the old Testament impossible to be given by divine Inspiration, such as the Approbation ascrib’d to the Angel of the Lord, of that abominably wicked and detestable Action of Jael the Wife of Heber the Kenite. If the rest of the Book were like that, I should rather suppose it given by Inspiration from another Quarter, and renounce the whole.
And earlier in his life, Franklin stated the Christian revelation was secondary to what God already revealed in Nature:
Now, that to promote the Practice of the great Laws of Morality and Virtue both with Respect to God and Man, is the main End and Design of the christian Revelation has been already prov'd from the Revelation itself. And indeed as just now hinted at, it is obvious to the Reason of every thinking Person, that, if God almighty gives a Revelation at all, it must be for this End; nor is the Truth of the christian Revelation, or of any other that ever was made, to be defended upon any other Footing. But quitting these things; if the above Observations be true, then where lies the Absurdity of Hemphill's asserting,
That Christianity, [as to it’s most essential and necessary Parts,] is plainly Nothing else, but a second Revelation of God’s Will founded upon the first Revelation, which God made to us by the Light of Nature.
John Adams likewise believed what man discovers about God from reason is primary all other sources of revelation, including the Bible, are secondary. From his letter to Jefferson Dec. 25, 1813:
Philosophy, which is the result of reason, is the first, the original revelation of the Creator to his creature, man. … no subsequent revelation, supported by prophecies or miracles, can supersede it.
Adams also made clear he believed the Bible was errant, and doubted the Bible contained the right version of the Ten Commandments:
When and where originated our Ten Commandments? The Tables and The Ark were lost. Authentic copies, in few, if any hands; the ten Precepts could not be observed, and were little remembered.
If the Book of Deuteronomy was compiled, during of after the Babilonian Captivity, from Traditions, the Error or Amendment might come in there.
-- John Adams to Thomas Jefferson, Nov. 14, 1813.
Adams further expressed his skepticism of the accuracy of the Bible's text when he wrote:
What suspicions of interpolation, and indeed fabrication, might not be confuted if we had the originals! In an age or in ages when fraud, forgery, and perjury were considered as lawful means of propagating truth by philosophers, legislators, and theologians, what may not be suspected?
-- John Adams, marginal note in John Disney’s Memoirs (1785) of Arthur Sykes. Haraszti, Prophets of Progress, 296. Taken from James H. Hutson, The Founders on Religion, p. 26.
To Adams, Jefferson, and Franklin, Christianity had been "corrupted," -- "the corruptions of Christianity" was a phrase coined by their spiritual mentor Joseph Priestley which he defined as the Trinity, Incarnation, Atonement, and plenary inspiration of the Bible. Miettinen mentions the King James Bible as central to American Christianity. But Adams named that version of the Bible as particularly corrupted:
We have now, it seems a National Bible Society, to propagate King James’s Bible, through all Nations. Would it not be better, to apply these pious subscriptions, to purify Christendom from the corruptions of Christianity, than to propagate these corruptions in Europe, Asia, Africa, and America!
-- John Adams to Thomas Jefferson, November 4, 1816. Taken from Hutson, The Founders on Religion, p. 143.
And of course we have Jefferson notoriously taking his razor to the Bible using his reason to judge which parts were genuine, which parts were corrupted. I focus on Adams by the way, to show just how mainstream these views were among the elite Whigs from which America's Founders were disproportionately drawn (but probably not mainstream among the general population). Jefferson has gained a reputation as some sort of outlier. And in many senses, he was: his politics were more radical; his intelligence was exceptional; he, along with Madison, would separate church and state more so than would most other Founders. Adams is rightly thought of as more politically conservative than Jefferson. However, on God's attributes, Jefferson and Adams were virtually agreed.
So when an air of mystery surrounds other key Founders, a strong reticence to explicate their religious specifics at a time when the institutional Churches expected public figures to profess orthodoxy, but many of them secretly believed in heterodoxy, absent evidence to the contrary, they probably believed as Jefferson, Adams, and Franklin did. James Madison was one such Founder. And in his notes preparing for the Memorial and Remonstrance he mentioned there are different kinds of Christianities, including Trinitarian and Unitarian, and that which believes the entire Bible is inspired, and that which believes only certain "essential parts" are divinely inspired.
The question is whether this unitarianism that held God primarily revealed Himself through Nature and that only parts of the Bible were inspired can be legitimately termed "Christianity," and whether its God is legitimately termed "the Christian God." So when Mr. Miettinen asks "in what sense are we not talking about a Christian God," I think I've outlined a very meaningful sense, and have strong grounds for claiming in my original essay that the key Founders posited a "rational, benevolent, unitarian deity who fit their republican ideals much better than the Biblical God could."