Just to be devil's advocate (yuk yuk), you can make a strong argument that our nation was based on science. First, Enlightenment thought and philosophy had a deep effect upon the Framers and the rationalist Constitution they produced. But more specifically, a lot of Madison's famous Federalist #10 bears a striking resemblance to Newtonian physics and its idea of vectors canceling each other out.
Remember that the revolutionary idea of Federalist #10 was that "factions" were less likely to abuse power in a large republic because there would be too many of them competing. According to Madision, they would essentially cancel each other out - just like Newtonian vectors.
I think that Federalist #10 is a pretty powerful indictment against America as a "Christian" nation, but not in the way Publius is saying. Rather, the underlying premise of Federalist #10 is a fear of power. This fear is generic, it isn't framed in a "but what if the Jews/Blacks/Blondes win elections" manner. That framework makes no sense if one believes in an absolute truth, like, say, Christianity. If one believes Christianity is "the way," then the objective of Federalist #10 would have been to demonstrate why the wrong people (Jews, Muslims, etc) won't gain power, not why nobody (Christian fundamentalists included) will gain too much of it. After all, if America was designed to be a "Christian nation" founded on Christian principles, then the structures of our government would rationally have been concerned with elevating their exclusive power and subordinating other potential threats. One impact of this is the suppression of democracy. I referenced this quote in a previous post, but I think it is very pertinent here as well:
To believe that a final resolution of conflicts is eventually possible...far from providing the necessary horizon of the democratic project, is something that puts it at risk. Indeed, such an illusion implicitly carries the desire for a reconciled society where pluralism would be superseded. When pluralist democracy is conceived in such a way, it becomes a self-refuting ideal because the very moment of its realization coincides with its disintegration.[Chantal Mouffe, "Democracy and Pluralism: A Critique of the Rationalist Approach," 16 Cardozo L. Rev. 1533, 1544 (1995)]
On a structural level, pluralism cannot coincide with the belief in one ultimate end result. Individuals can, of course, believe passionately that one way is the "right way" while still recognizing that the state should remain neutral. However, states cannot simultaneously affirm one path as totally true and beyond debate and yet still allow for democratic deliberation. If America was a "Christian nation," it would have to recognize the universality of Christ's salvific event and thus view its unsaved citizens as "impure" or "deviations." It would also have to support missionizing activities against them, if not more hostile actions designed to get them to convert. Furthermore, if the crucifixion and resurrection were seen as the penultimate events in human history (which is the essence of the Christian narrative), then any political or social theory working outside that tradition (or that couldn't be incorporated in it) would have to be rejected on face. In such a world, it is simply impossible to argue that religious minorities could be equal members of the political community--the red line of what represents a legitimate democracy. Democracy is more than just having a vote--it presumes some manner of equality under law in which all members of the community have a voice in the system. Furthermore, as Mouffe points out, democracy is fundamentally indeterminate, it cannot affirm any particular end-values beyond what is necessary to keep the system itself running. These values are, for better or for worse, secular (free speech and press, equality under the law, right to vote, respect for the Other, etc).
Ian Reifowitz wrote a spectacular article in The New Republic outlining the way Christian universalism, when transplanted from the religious sphere and morphed into a political ideology, is effectively oppressive and anti-pluralist:
Christian conservatives...are not separatists: They sincerely care about the souls of all people, and their theology, going back to St. Paul, calls for them to seek new members across lines of race, ethnicity, culture, and religion.
But when this universalism enters the political arena, it has the same effect as radical multiculturalism. Anyone is welcome to join adherents of the theocratic right and adopt their beliefs, but anyone who does not--gays, feminists, proponents of abortion rights, non-Christians--ultimately faces second-class status in the America they plan to build. This is a rejection of pluralism that is every bit as fundamental as the rejection of pluralism preached by the radical multiculturalists: Both would end in large swathes of the American population severed from our national identity.
This is not to single Christianity out, loads of faiths and practices would, in effect, represent the same sort of anti-pluralist ideology. The reason we have to focus our attention on Christianity in particular, however, is because in America and in much of the world Christianity has a hegemonic dominance over other religion that makes it far more powerful--and more dangerous--than other like-minded groups. Put another way, we don't have to worry about any anti-pluralist stirrings in an obscure Nevada cult--but when that anti-pluralism is coming from the largest religion in the world, history reminds us of the need to take notice.
Christian theologians, especially those who have written in the post-Holocaust field, have begun to come to terms with this fact. Gregory Baum notes:
[P]olitical events of world history have made the churches reconsider the meaning of their missionary activity or evangelization. They have been made to see how closely their missions have been associated with the extension of Western power and Western culture. The protesting voices from the Third World and the social critics in the West have convinced many churchmen that the doctrine of the church's mission has legitimated the invasion of the continents by the Christian nations. For many centuries, the church regarded the expansion of the white man as part of God's providential design. The missionary followed the soldier and merchant. The confidence with which whites gained power over the continents, drew the peoples of the world into institutional structures the centers of which were in the West, and organized the resources of the earth so as to make by far the greater share available to Christian nations, cannot be separated from the Christian claim that the church is the unique instrument of salvation and that it is destined to embrace all the peoples of the world. We do not suggest, of course, that the Christian church was the acting cause behind the expansion o the Western nationals. What we do claim is that the imperialistic invasion and appropriation of the continents, caused by a variety of economic, political, and cultural factors, was sanctioned by the church's understanding of world history, with the Christian commonwealth at the center and the non-Christian peoples on the periphery, destined to become Christian in due time.
Thanks to a keener social conscience, the churches have become sensitive to the political meaning implicit in their missionary action. The hidden implication of their claim to unlimited universality is the spiritual suppression of all other religions and of the various cultures that have been nourished by these religions. ["Rethinking the Church's Mission after Auschwitz," in Auschwitz: Beginning of a New Era, Eva Fleischner, ed., (NY: Cathedral of St. John the Divine, 1977), pp. 113-28, 114]
At root, a Christianity which cannot accept the validity of other ways of seeing the world (IE, those who do not accept Christ as savior and/or do not consider themselves to be irredeemably "fallen" without him) is a Christianity that will never be able to break out of a belligerent stance. It will never be able to completely shed its anti-Semitic past, and it will never be able to reverse the disturbing trend of imperialism and colonial domination which has followed Christian missionization for centuries.
Members of the Christian Right need to come to terms with a simple fact: America cannot be both a Christian nation and a democratic nation at the same time. This is not to say one cannot be a good Christian and a good American at the same time--we are talking solely about making America, as a state, into a Christian nation, not about the legitimacy of the views of private actors. Christian viewpoints are perfectly legitimate to hold, and nobody has any business saying that Christian values should be excluded from the citizenry (as some leftist commentators regrettably have advocated). The question is whether these values can be transported from the private sphere into the public, IE, whether Christian values should supplant the democratic values of, among other things, equality under the law. I'd entirely understand if they chose Christianity over democracy--after all, religion has been known to demand that sort of loyalty. But they have to recognize such a statement is an act of war against every value America stands for.