The Court focused on the notion that students can choose not to recite the Pledge. Yet, in Lee v. Wiseman, the Court had ruled that students were coerced at a graduation ceremony where a prayer was included. When Newdow cited Lee v. Wiseman, O'Connor (and Kennedy) kept emphasizing the notion that case was about a
prayer and that the Pledge isn't a prayer.
That's where Newdow blew it, imho.
His immediate response should have been that, to an atheist,
there's no such thing as a prayer. Thus, if it makes such a distinction, the Court itself is employing a faith-based test. In effect, the Court commits the fallacy of an assumed conclusion in making any such distinction. They stacked the deck. (It's an error in fact.)
(The NYTimes has published some transcript excerpts
here.)