James F. McGrath, Associate Professor of Religion at Butler University, Indianapolis, nails the problem with the "Christian Nation" thesis as articulated by Barton, Marshall, Federer, et al.:
It seems unlikely that at any point in the past the vast majority of inhabitants of the United States were devout Christians with a personal faith, as opposed to nominal Christians for whom their Christianity consisted largely of a "tribal identity" including churchgoing and assenting to some doctrinal beliefs and moral precepts.
Does it not seem ironic, then, that the notion of American having once been a "Christian nation", and nostalgia for that bygone golden age, is found largely among Evangelicals, those very Christians who emphasize the need for a personal faith, and the inadequacy of a Christianity that consists merely of church attendance, denominational affiliation, or even moral living?
Am I missing something? Why would the very Christians who deny the adequacy of such nominal Christianity today, depict its heyday as a sort of golden age for American Christianity?
That's the problem: There was no Golden Age. Arguably the evangelical view of the Bible teaches there never will be a Golden Age until Christ returns as their faith is a "narrow path." Roger Williams, ironically, understood this and in doing so was one of the first Christian political leaders to reject the "Christian Nation" thesis and, consequently, promote "religious liberty."
Williams was clear, it is only by rejecting that a nation is "Christian" in a civil, governmental, covenant sense (in the sense that the Puritans like John Winthrop articulated and tried to put into action) that government could recognize religious liberty. And key to Williams' assertion was the inevitable existence of large numbers (perhaps, probably a strong majority!) of "unregenerate" (i.e., nominal Christians) existing in any nation, even those whose population consider themselves "Christian." The inevitable existence of large numbers of unregenerate everywhere before Christ's return makes the idea of a "Christian Nation" blasphemous.