Kristo Miettinen raises an extremely important point about my excluding America's key Founders from the definition of Christianity.
But here you exclude Hamilton from the extension of the label “Christian” by choosing a fairly serious specific definition of “Christian”. It is one thing for Calvinists and Catholics and whatnot to have tight definitions of “Christian” as they assess one another in sectarian squabbles, but quite a different matter to apply tight definitions when looking at historical figures in historical context.
Think, for instance of the early colonists; Quakers, Puritans, splinter groups of all sorts. Why did they come to America? Broadly speaking, to escape religious persecution. And why were they persecuted? For their unorthodoxy, by the standards of their day and home countries. Do we really want to look at history through tightly selective lenses, so that we deny that the various early colonists were Christian because of their unorthodoxy?
When viewed from a secular historical perspective, shouldn’t we group together a fairly broad swath of thought under the label “Christian”? If we do, then many of the theistic intellectuals of the late 18th century, those who are at worst ambivalent about the special character of Christ and his teaching (and at best willing to accept that there was something unique, unrepeatable, dare we say “divine” about Christ), are broadly speaking Christians.
I've struggled with this point before, particular on the question of whether Mormons are Christian. In a broad sense, yes, America's key Founders [Washington, Adams, Jefferson, Madison, and Franklin], Mormons, Jehovah's Witnesses, cafeteria Christians, theologically liberal Christian Churches that perform same sex marriages are all "Christian." Statistics show that 80% of America qualify as "Christian" under this understanding as did around 99% of Americans during the Founding era. Anyone who calls himself a "Christian" qualifies under this label, and as a Catholic who never went beyond baptism and does not go to church, I could too if I decided to call myself "Christian."
Evangelicals and Catholics, though they have their own disagreements, have no problem more narrowly defining what it means to be a Christian. Given that orthodox Protestants have always accepted the legitimacy of the early Church -- the one that produced the Nicene Creed, which they view as not the same Church against which Luther protested -- evangelicals and Catholics have always had a common ground in traditional orthodoxy.
I think I tend to define Christianity so narrowly because of my avocation studying the philosophy of America's Founding, particularly as it relates to religion. The historical and political dispute over the ideological underpinnings of America's Founding is about something more than just the demographics of America, which few dispute -- about 99% of the population were "Christians" in some broad sense of the term as are about 80% today. Yet, one study of Founding era America showed that only 17% of America's population were actual Church members, that the taverns on the weekends were more crowded than the Churches on Sunday morning. James H. Hutson disputes the figure and states that as many as 70% may have been Church members. Today about 45% of the population regularly attends Church.
If "Christian" defines so broadly as to include all of the unchurched, nominal, theologically liberal, cafeteria, unitarian, universalist and perhaps even agnostic or atheistic folks, there is really not much to argue about. America is a Christian Nation and almost all of us are Christians including every single liberal Democratic candidate and all of those "Christian" Churches that would gladly marry same sex couples, and ministers who disbelieve in the Divinity and Resurrection of Jesus, and all of the miracles in the Bible.
Perhaps that is the proper definition of "Christian," but for the research that I do, that definition doesn't suffice. Though what I'll try to do is qualify the term "Christian" with "orthodox" whenever I make it clear that America's key Founders were not "Christian."