You can read an original copy from googlebooks here or a nice reproduction here. Mayhew was one of the most influential of the pro-revolutionary preachers of the Founding era (that's why he's important to study). Interestingly, he turned out to be a "unitarian" of the Arian bent, something orthodox Christians believe "heresy" that disqualifies someone from status as a "Christian."
Mayhew probably felt comfortable with the label "rational Christian." That is, he promoted the excessive use of free inquiry, reason and natural law in matters of religion. Such method led Mayhew to conclude that orthodox Trinitarian doctrine was a product of erroneous man-made ecclesiastical authorities.
The standard that elevates reason and free inquiry over ecclesiastical authorities can deconstruct not just orthodox doctrine like original sin, trinity, incarnation, atonement, but the biblical canon itself. Arguably ecclesiastical authorities selected the biblical canon. So how do we know we have all of the right books? Likewise, how do we know the books in the Bible are God's infallible Word? Perhaps ecclesiastical authorities inserted erroneous "interpolations" in the Bible?
It's important to keep this paradigm in mind for the following reason: Anti-Roman Catholic bigotry was something that certainly united "Protestants" of the liberal unitarian and conservative evangelical bent during the Founding era. Today the "Christian America" crowd -- comprised largely of Sola-Scriptura evangelicals and fundamentalists -- tend to dismiss the anti-ecclesiastical rhetoric of the American Founding as mere anti-Romanism, while positing the Bible (that is the canon) -- the inerrant, infallible Word of God (complete with orthodox doctrines like original sin, trinity, atonement, eternal damnation) -- as the source of American political theology. Not so. The anti-ecclesiastical, free inquiry method of "rational Christians" like Jonathan Mayhew, Charles Chauncy, and John Adams led them to reject not just original sin, trinity, atonement, eternal damnation, but arguably the infallibility of the biblical canon itself.
All the while they still believed themselves "Christians," that Jesus was Messiah (or King) and that God revealed Himself to man in His Word.
Over at American Creation, an interesting dialog on this very issue is taking place among Gregg Frazer, Tom Van Dyke and King of Ireland. TVD and others disagree with Gregg's assertion that the political theology of Mayhew, Chauncy, Priestley, J. Adams and others represented reason trumping revelation. That is, these Founding era figures believed while God did speak to man in biblical revelation, ultimately the Bible was partially inspired, errant, and that man's reason (i.e., THEIR reason) trumped what was written in the Bible's text.
Now, that's quite a contentious assertion, with some loaded premises. But in fairness to Gregg, many folks, for good reason, believe in those loaded premises and here they are: The biblical canon -- by itself and nothing more -- is God's complete, inerrant, infallible Word. This canon, moreover, clearly teaches doctrines like Trinity, Incarnation, Atonement, and Eternal Damnation. And, one of Gregg's pet favorites, that Romans 13 and every other verse and chapter of the Bible teach unlimited submission (though not necessarily obedience) to governmental authorities.
So along come Jonathan Mayhew, Charles Chauncy, Joseph Priestley, John Adams, Thomas Jefferson and company -- men who called themselves "Christians," -- all of whom (except Jefferson) believed in the Resurrection of Jesus of Nazareth (not of the 2nd person in the Trinity, but of God doing for His inferior not fully divine Son what He may one day do for all good men), men who promoted the excessive use of natural reason in religion, denying original sin, the trinity, incarnation, atonement, eternal damnation, and that Romans 13 demands categorical submission to government.
I understand exactly why Gregg and others sympathetic to the premises of historic Christianity (not just evangelicals, but Roman Catholics, and orthodox Anglicans) would argue this is "man's reason" trumping "revelation," even if others might dispute the analysis.