Bellah, Robert. "Civil Religion in America." From Alexander, Jeffrey C., and Steven Seidman. Culture and Society: Contemporary Debates. Cambridge [England]: Cambridge University Press, 1990.
Originally published 1970
Examples from the Kennedy inaugural, to the Declaration of Independence, to Lincoln's 2nd inaugural and Gettysberg Address, back to LBJ demonstrate the continuing place of God (though never, explicitly, Jesus) in America's self-perception.
"...the separation of church and state has not denied the political realm a religious dimension." Bellah distinguishes between personal belief, worship, and ritual which are seen as private affairs and the more common elements of religious ideas that spread throughout the fabric of American life. The inauguration affirms the religious legitimation of the President. (263)
America has long conceived of itself as an extension of and a modern version of Israel, and a nation created by believers to be a light to the world. It remains so as Bellah writes in 1970 (earlier? during LBJ?), in the midst of the Cold War.
Until the Civil War, the Civil Religion focused on the Revolution as the ultimate act of "Exodus" for the U.S. But the Civil War inevitably undermined this vision. Lincoln's use of "birth" and related words throughout the Gettysburg address, as well as the myth of Lincoln himself, reveals the death-sacrifice-rebirth meaning the Civil religion took from the Civil War.
The Civil religion remains alive, for better or, as Bellah concludes, for worse: though he certainly buys in to the conception of the Cold War as a good-vs-evil endeavor, LBJ avoided using the Civil religion to claim God's favor in Vietnam but others haven't been so hesitant.
Could we have an agnostic President? Bellah is skeptical.
"If the whole God symbolism requires reformulation, there will be obvious consequences for the civil religion, consequences perhaps of liberal alienation and of fundamentalist ossification that have not so far been prominent in this realm." (272) He thus anticipates the divide between liberals and fundamentalists that has shaped politics in the last 30 years.
Bellah assumes an continuing difference between Civic Religion and personal, private beliefs. However, I think this divergence, while perhaps not beginning in the 20th century, has certainly been exacerbated by the cultural revolution sparked by Freud, described by Rieff, and increasingly lamented by Bell, Lasch, etc. etc.