Carter argues against it again (as he oft-does every few years) here.
I think most Christians would agree that there is a vast and unbridgeable chasm between a deistic civil religion and orthodox Christianity. But the civil religion that our fellow citizens embrace is not the type Rousseau had in mind. It is very much a view that is rooted in the concept that America is a Christian nation (or at least a Judeo-Christian nation). For them, the “In God We Trust” on our coins might as well say “In Jesus We Trust.” The State is not only subordinate to the one true Sovereign (and don’t let the capitalized noun fool you—we’re still talking about Jesus here) but is expected to conform to his standards. Although this view can lead people to use Christianity to promote Americanism, more often it simply leads to criticism of the nation’s flaws. The fact that the country continually falls short of God’s standards is a constant annoyance for those who believe that the founding documents were wholly derived—at least in principle—from the Holy Scriptures. (Think I’m exaggerating? Talk to some of these folks and see if you don’t get the impression that they think the Constitution was inspired more by the Gospel of John than by John Locke.)
Those of us who champion a role for religion in the public square, however, cannot fully embrace this Christianized concept of civil religion. If we claim, as our friends and neighbors believe, that “under God” refers only to the Christian conception of God then we are either being unduly intolerant or, more likely, simply kidding ourselves. Do we truly think that our fellow Hindu, Wiccan, or Buddhist patriots are claiming to be under the same deity as we are? We can’t claim, as the Apostle Paul did on Mars Hill, that the “unknown god” they are worshiping is the God of Abraham, Isaac, and Jacob. The Pledge is, after all, a secular document and the “under god” is referring to the Divinity of our country’s civil religion. Just as the pagan religion of the Roman Empire was able to incorporate other gods and give them familiar names, the civil religion provides an umbrella for all beliefs to submit under one nondescript, fill-in-the-blank term.