I don't buy Geoff Nunberg's argument that if the meaning of under God were compositional it should occur frequently in other contexts. A phrase will occur frequently in various contexts if people have frequent occasion to express the idea it expresses and if there are not very many ways to express that idea. The rarity of under God is probably due to the fact that these conditions are not satisfied. First, it isn't all that often that people feel the need to express this idea. Nobody wants to express the idea that the the United States is physically located beneath a physical God because to my knowledge nobody believes that. And those people who believe that the United States has been, is, or should be "under God" in the sense of being watched over by God or ruled by God or conforming to God's will, are all, in my experience, Christians, and when they express such ideas they speak in more specific terms, e.g. about a Christian nation.
This brings us to the second condition. There are lots of ways of expressing this sort of idea. Many of them wouldn't be good candidates for this particular context because they couldn't be made to fit the syntax or the metrics. Remember, the words under God were an addition to an existing text, which constrained the possible choices of phrasing. An additional constraint is that, although it may be possible to get away with non-denominational deism, it is pretty clear that a reference specifically to Christianity would have been much more problematic and more likely to be struck down by the courts. So it seems very likely to me that under God is not found in other contexts simply because nobody has felt the need to say the same thing subject to the same syntactic, metrical, political, and constitutional constraints.
We can see this by considering the phrase with liberty and justice for all. That phrase too appears to be unique to the Pledge of Allegiance. The only other hits that Google turned up (and that I could spare the time to look at) are obvious references to the Pledge, such as the title of a book. Yet nobody thinks that this phrase is an idiom. It's a perfectly compositional phrase that happens to occur only in the Pledge of Allegiance and references to it.
Indeed, suppose that under God were an idiom. Why wouldn't it occur in other contexts? Except for deadwood known only to scholars, idioms, like morphological irregularities, have to be fairly frequent or nobody would learn them. I submit that the plausible answer is because nobody felt the need to express whatever it is that this means subject to similar constraints.
It seems to me that there are only two possibilities here. One is that under God is compositional and has one of the several meanings in which it presupposes the existence of a single deity. In this case, it is unconstitutional. The alternative is that it is an idiom, created at the time it was added to the Pledge, whose meaning we really don't know. I find that highly implausible, because it means either that the people who proposed the addition and the legislators who voted for it didn't know what it meant or that they knew but have somehow failed to pass this information on to us. Furthermore, it's hard to believe that so many people would care so much about retaining it if it had no meaning. Indeed, if its meaning is really unknown, given that the campaign to insert it was led by the Knights of Columbus, we wouldn't expect such strong support from evangelical Protestants for retaining it. Instead, I would expect indifference from some and support for removing it from others, who would see it as a Papist plot, probably with a Satanic meaning. In any case, if it really is an idiom of unknown meaning, it may not be unconstitional, but it has no place in the Pledge because it is meaningless.