This is one message I get from an excerpt of Nathan Hatch's The Democratization of American Christianity. Hatch is, by the way, president of Wake Forest University and one of the premier scholars of Religion and the Founding Era.
We see in the writings of our key Founding Fathers support for the Protestant Reformation. However, they also supported Enlightenment and the notion that religion needed to further reform to conform to the tenets of Enlightenment. As George Washington wrote: "I was in hopes, that the enlightened and liberal policy, which has marked the present age, would at least have reconciled Christians of every denomination so far, that we should never again see their religious disputes carried to such a pitch as to endanger the peace of Society."
Hatch's excerpt shows how the notion of sola scriptura and further reform ultimately resulted in denying historic Christian doctrines. This is notable because many of the ministers that he references who did this happened to be the most influential pro-revolutionary preachers and the ones most likely to capture the minds of our key Founders. They were also theological unitarians and universalists. These figures were the most "Enlightened" preachers. They were essentially preaching "infidelity" from their pulpits. As Hatch writes:
DENYING HISTORIC CHRISTIAN DOCTRINE FROM THE "BIBLE ALONE"
The first Americans to underscore the right of private judgment in handling Scripture were, oddly enough, ministers who opposed the evangelical tenets of the Great Awakening. As New Lights in New England worked to make people more theologically self-conscious, often by rewriting church covenants to include strict doctrinal standards, theological liberals increasingly resisted strict creedal definitions of Christianity. The future president of the United States, John Adams, like many of his generation, came to despise theological argumentation. He reported in his diary in 1756,
"Where do we find a precept in the Gospel requiring Ecclesiastical Synods? Convocations? Councils? Decrees? Creeds? Confessions? Oaths? Subscriptions? and the whole cart-loads of other trumpery that we find religion encumbered with in these days?" 
To gain leverage against the entrenched Calvinism of the Great Awakening theological liberals redoubled their appeal to depend on the Scriptures alone. "Why may not I go to the Bible and learn the doctrines of Christianity as well as the Assembly of Divines?" the prominent Boston clergyman Jeremy Belknap asked in 1784. Simeon Howard, a more liberal minister, exhorted his colleagues to "keep close to the Bible" and to "avoid metaphysical additions." He also advised clergyman to "lay aside all attachment to human systems, all partiality to names, councils and churches, and honestly inquire, 'what saith the scriptures.'" 
Charles Chauncy, pastor of Boston's First Church for sixty years (1727-1787), is the most prominent example of an exclusive appeal to Biblical authority in order to unravel theological orthodoxy. Chauncy was persuaded to emphasize Bible study by reading the works of English divines, such as Samuel Clarke's The Scripture-Doctrine of the Trinity (London, 1712) and John Taylor's The Scripture-Doctrine of Original Sin (London, 1740). Both authors used a "free, impartial and diligent" method of examining Scripture to JETTISON, respectively, the doctrines of the Trinity and of Original Sin. 
During the 1750s, after the Great Awakening, Charles Chauncy spent seven years engaged in the approach to Bible study expounded by these English authors. In the spring of 1754 he wrote to a friend,
"I have made the Scriptures my sole study for about two years; and I think I have attained to a clearer understanding of them than I ever had before."
His studies led him to draft a lengthy manuscript in which he REJECTED the idea of eternal punishment and embraced universalism. He kept this work in his desk for over a quarter-century, its conclusions, he confessed, too controversial "to admit of publication in this country." He was nearly eighty when he finally allowed a London publisher in 1784 to print The Mystery Hid from Ages and Generations...or, the Salvation of All Men. To justify his conclusions, Chauncy relied on the biblical force of his argument, "a long and diligent comparing of Scripture with Scripture." He explained to Ezra Stiles, "The whole is written from the Scripture account of the thing and not from any human scheme." This unorthodox biblicist would have been gratified indeed by the reaction of one minister who, finding the book's arguments convincing, wrote,
"He has placed many texts and passages of Scripture in a light altogether new to me, and I cannot help thinking his system not only rational, but Scriptural." 
Well into the nineteenth century, rationalistic Christians -- many of them Unitarians and Universalists -- argued against evangelical orthodoxy by appealing to the Bible. Unitarian Noah Worcester's arguments were typical. He challenged people to think for themselves, to slough off a "passive state of mind" that deferred to great names in theology. "The Scriptures," he declared, "were designed for the great mass of mankind and are in general adapted to their capacities."
Worcester assumed that mysteries such as the Trinity would be discarded by a disbelieving public once people learned to explore the Bible for themselves. He recounted his Unitarian conversion in a book appropriately entitled Bible News of the Father, Son, and Holy Spirit (Concord, NH, 1810).  In the same vein, Charles Beecher defended his rejection of his father Lyman's orthodoxy by renouncing "creed-power" and raising the banner of "the Bible, the whole Bible, and nothing but the Bible."  By the 1840s, however, when Charles Beecher had moved beyond the pale of orthodoxy, a different and decidedly more evangelical notion of biblicism had taken root within American culture.
Read the whole thing here.