Strictly on this rhetorical basis, Newdow should win. But in this case, as with most complex cases, it will come down to the merits of the arguments presented, and the particular personalities of the individuals involved, including the lawyers for the government's position, as well as the particular personalities of the sitting Supreme Court members. In this case, there is one worrisome technical argument against Michael Newdow, which is that he doesn't have full-time custody of his daughter, and therefore his standing to even try the case is questionable. But perhaps this should have been sorted out at a lower court?
There are also many political reasons why Newdow seems likely to lose, and we have no way of knowing how important these will be for the Court in their deliberations in the weeks to come. And pragmatically, this type of case antagonizes conservatives without much payoff. "Under God" in the Pledge is more benign, in my view, than refusing the right to marry to same-sex couples; I would rather force this kind of showdown when major rights are on the line. (Of course, there's only so far you can go with pragmatism. Chances are, the Court will soon hear a gay marriage case as well, and if it is tried well and they are interpreting the law rigorously, that showdown will happen too. But I digress.)
The actual substantive arguments from the government (Ted Olsen) are interesting. Leon Wieseltier, in his recent New Republic piece, summarizes some of them:
In the Pledge of Allegiance, the government insisted, the word "God" does not refer to God. It refers to a reference to God. The government's argument, as it was stated in the brief filed by Theodore B. Olson, was made in two parts. The first part was about history, the second part was about society. "The Pledge's reference to 'a Nation under God,'" the solicitor general maintained, "is a statement about the Nation's historical origins, its enduring political philosophy centered on the sovereignty of the individual." The allegedly religious words in the Pledge are actually just "descriptive"--the term kept recurring in the discussion--of the mentality of the people who established the United States. As Olson told the Court, they are one of several "civic and ceremonial acknowledgments of the indisputable historical fact that caused the framers of our Constitution and the signers of the Declaration of Independence to say that they had the right to revolt and start a new country."
I tend to agree with Wieseltier that most of these fall apart under close inspection, because "under God" cannot be merely historical or descriptive. I was also intrigued by Wieseltier's invocation of Lockean vs. "absolute" tolerance, following Justice Breyer's point that "under God" is more "ceremonial Deism" than it is religion:
In fact, Breyer was advocating the Lockean variety of toleration, according to which it would be based on a convergence of conviction, a consensus about the truth, among the overwhelming majority of the members of a society. The problem with such an arrangement is that the convergence is never complete and the consensus is never perfect. Locke himself instructed that "those are not at all to be tolerated who deny the Being of a God." The universal absolute is never quite universal.
Is Wieseltier's version of Locke quite correct? Hm, I remember the theological perspective in Locke's "Letter on Toleration," but not the intolerance to the overt atheist. Will need to check Locke...
Wieseltier has another high-powered philosophical moment -- an invocation of Immanuel Kant:
After Kant explained that we can have no direct knowledge of the thing itself, and certainly not of God, religious statements have tended to be not propositions of fact, but propositions of value--expressions of inner states that are validated by the intensity of the feeling with which they are articulated. Certainty weirdly became an accomplishment of subjectivity. Kant thought that he secured religion by placing it beyond the bounds of knowledge. But this was a false security, because the vocabulary of theism continues to point to more than emotion or experience or tribe or culture. Prayer in particular remains, at least at the level of its language, an address in the second-person singular to an entity that is not oneself. Theology, if it wishes to be regarded as more than a cerebral fantasy, cannot be content to have its basis in the imagination; it must appeal to the authority of philosophy if it is to continue to speak about what is true.
Here I find Wieseltier's summary of Kant's argument helpful (I take it he is talking about Religion Beyod the Limits of Reason Alone, though I haven't yet confirmed). But I find his critique of Kant's relegation of religious belief to the realm of subjectivity questionable.
Wieseltier clarifies the relevance of Kant when he writes, a little later: "There is no greater insult to religion than to expel strictness of thought from it." We've seen this line of thinking before -- religion must be completely removed from politics in order to protect it (indeed, Jewish and Christian clergy have submitted a brief in support of Newdow on the grounds that the Pledge potentially causes students to violate the Sixth Commandment: "Thou shalt not take the Lord's name in vain.")
But the tradition of vague theism with very strong functional separations of church and state has provided the balance that has made American secularism so stable. I worry about upsetting this balance. In actuality, the willingness of the courts to involve in certain matters of religion has provided a net benefit to our society -- the classic example of this might be the 1879 case (Reynolds v. the United States) where the government banned polygamy for Mormons, despite the explicit encouragement for the practice in the Mormon religion. In the long run, one could argue, this act of intervention has been beneficial both to the "greater common good" of American society and to the Mormon Church itself.
Does Newdow's insistence on absolute atheism really threaten that balance? I'm still working on it.