But what is the “widely-held, common idea of what ‘under God’ in the Pledge means”? That is Nunberg’s point.
Does it mean, as Lincoln originally used it the Gettysburg Address from which it was consciously lifted, “God willing?” “We will be one nation, God willing”? An apt sentiment in the midst of a Civil War, not so much ninety years after the fact. (Actually, Lincoln used in the context of a “new birth of freedom,” not “one nation.")
Does it mean, “one non-communist nation”? This was the political motivation for adding the phrase to the Pledge in the 1950s.
Does it mean we are a nation that respects people’s innate political rights, those “endowed by [our] Creator,” using “God” in a Jeffersonian, Deistic sense?
Does it mean we are a nation that respects and tolerates all spiritually inclined people, regardless of their religion, but that atheists should get the hell out?
Does it mean we are a Roman Catholic nation? After all, it was the Knights of Columbus who were behind the phrase’s inclusion.
Does it mean we are a fundamentalist Christian nation? (Or Anglican, or Jewish, or Islamic, or Hindu, or Buddhist, for Flying Spaghetti Monster--take your pick)
The phrase means whatever you want it to mean. Which, in the context of a loyalty oath, is pointless.
I would go further. A lot of political (and diplomatic) phrasing is deliberately designed to be ambiguous, and this is a case in point. By using phrases with slippery meanings, you can get a broad base of people to agree to the phrase, while they may hold very different and even opposing viewpoints on its precise meaning. You get temporary agreement on weasel wording and keep kicking the can down the road until it doesn’t matter any more, then you drop the whole issue. But sometimes it backfires and you end up creating a worse problem.