At American Creation, Tom Van Dyke asks them. Of them:
---And the old standby, What is "Christian?" Can you be "Christian" if you believe the Bible is the direct Word of God? If you believe Jesus is the Messiah, although not the Second Person of the Holy Trinity?
---And who decides the answer to this question? Trinitarian clergy? Theologians? Sociologists? Historians?
---Was there a God of the Founding?
---Was His name Providence?
---Is this "theism," or is "theism" just a slippery term for what is the uniquely monotheistic, providential Creator-God who endowed men with certain unalienable rights, one who is unmistakably "Judeo-Christian," at least compared to all of man's other gods?
---What might Judeo-Christian mean? Anything? Everybody seems to know what it means, so does that mean anything?
I focused on these because they parallel questions James Madison asked in his notes preparing for the Memorial and Remonstrance. Madison asked:
3. What is Xnty ? Courts of law to Judge.
4. What edition: Hebrew, Septuagint, or Vulgate ? What copy what translation ?
5. What books canonical, what apocryphal ? the papists holding to be the former what protestants the latter, the Lutherans the latter what the protestants & papists ye former.
6. In what light are they to be viewed, as dictated every letter by inspiration, or the essential parts only ? Or the matter in general not the words ?
7. What sense the true one for if some doctrines be essential to Xnty those who reject these, whatever name they take are no Xn Society?
8. Is it Trinitarianism, Arianism, Socinianism ? Is it salvation by faith or works also, by free grace or by will, &c., &c.
9. What clue is to guide [a] Judge thro' this labyrinth when ye question comes before them whether any particular society is a Xn society ?
10. Ends in what is orthodoxy, what heresy. Dishonors Christianity.
By this time many leading light "Protestants," Madison perhaps among them, began to argue things like Arianism, Socinianism, salvation through works, and a Bible where only the "essential" parts (not the whole thing) were inspired, under the auspices of "Christianity."
Yet others -- the "orthodox" -- maintained believers in these positions "whatever name they take are no Xn Society."
Madison didn't want judges resolving this issue. And they would if government gave aid to "Christianity" generally but not "other" religions.
[This is, ironically, exactly what happened in Mass. and what led to their disestablishment, the last state to do so. In the Dedham decision, Unitarian judges decided Unitarianism was "Christianity" and hence eligible for state establishment aid. To the orthodox that poisoned the well; so they got rid of their state establishment of "Protestant Christianity."]
If the Supreme Court ruled the Constitution permits aid to "Christian" but not other religions, one easy solution would be simply call yourself a "Christian" and get that aid. You can be an atheist, a Muslim, a Jew, just call yourself a "Christian" and you are eligible for government support.
And that relates to another dynamic behind the "Christian Nation" debate. No one argues America wasn't and isn't a "Christian nation" in a nominal or demographic sense. No one argues, for instance, the Founders were predominantly Muslim.
98% of Americans thought of themselves as "Christians" as do roughly 80% today. These include, not just Pat Robertson and the Pope, but Chris Hedges, Andrew Sullivan (who it might surprise you, is orthodox in his Christology), Barack Obama and Mitt Romney.
Plenty of deistic and agnostic minded folks consider themselves "Christians" for heritage, cultural and demographic reasons. I am a baptized Roman Catholic (but went no further). Arguably, I could, but I don't, call myself a "Christian-Agnostic." Or a non-practicing Roman Catholic-agnostic.
Rather, we argue over a tighter, more meaningful definition of "Christian," AND how "Christianity" (however that theology defines) informed the principles of the Declaration of Independence, the US Constitution, and Federalist Papers and other aspects of life during Founding era America. Further, we argue over how the Founders THOUGHT government and religion should intersect.