The transcript of the oral arguments for the Pledge/Under God Case is up and it's fairly straightforward easy reading even for the layperson. The school district (with an assist from the Solicitor General, Ted Olson) basically focused on the standing issue -- the mother has custody, so it's up to her to challenge the policy.
Justice Kennedy challenged Newdow right away on this point as well, but Newdow responded rightly that yes, the mom can raise the child as she likes, but he also has the right to argue that the school has no right to stack the deck against him like this. Justice Kennedy in particular thought Newdow was ignoring that the force of the lawsuit would largely fall on his daughter, whose interests aren't directly at issue here. [Newdow is claiming his rights are harmed because the state is coercively injecting religious doctrine as part of her education and therefore demeaning her view of his religion.] All the same, even Kennedy was somewhat hesitant to accept Newdow had no standing -- the possible result of such a principle is troubling.
The school district lawyer quickly added in his brief rebuttal that "under God" was not religious, but more political philosophy, philosophy students are educated in along with respect for diversity. I don't recall being schooled in the natural rights philosophy behind the words "under God" in third grade, but maybe these days it is different. Olson had a bit more time to address this point, in part saying it is an "acknowledgment of the religious basis of the framers of the Constitution."
He also quickly noted that "God" is not the same as "Jesus," the former is nonsectarian and wider used. The problem is that he mentioned "Lord" as a form of "God," and "Lord" is used sometime (including in the date of the Constitution) in a way that clearly suggests "Jesus" is being referred to. This sort of thing, including trying to argue that belief in God really isn't sectarian was generally well attacked by Newdow, attempts to get him to say the use here is "generic" or "tepid," notwithstanding. He also inserted a good public comment from the President "that when we ask our citizens to pledge allegiance to one nation under God, they are asked to participate in an important American tradition of humbly seeking the wisdom and blessing."
Newdow ended well. He reminded everyone of the discrimination against atheists still prevalent today, as it was when the words "under God" were added in 1954 [this latter point brought about the now famous applause]. Newdow next explained the difference between the Establishment and Free Exercise components of the First Amendment: "[T]he Free Exercise Clause has never meant that a majority may use the machinery of the state to practice its beliefs." He quickly summed up why the inclusion of "under God" fails to meet the basic tests now in place to determine First Amendment violations. [One brief argues the inclusion is pretty generic so if it is made clear the children can say the Pledge with or without the words, all would be okay. It isn't really "generic" (especially given the original and often still current intent) and the usual peer pressure sort of problems would still apply. Good try, but no.]
And ended eloquently: "I'm hoping the Court will uphold this principle so that we can finally go back and have every American want to stand up, face the flag, place their hand over their heart and pledge to one nation, indivisible, not divided by religion, with liberty and justice for all." The alternative is a coercive religiously sectarian ceremony different in many ways than mention of God on coins or the like -- the child is directly asked to do something, something that divides not only the nation but a daughter from her father along religious lines.
Ironically, the only real mention of the fact that not just atheists are upset by the inclusion of "Under God" came during the rebuttal by the school district. Justice Stevens, lifting a point from an amicus brief on behalf [links provided to various briefs] of 32 Christian and Jewish clergy ministers, asked: "If the religious portion of the pledge is not intended as a serious affirmation of faith, then every day government asks millions of school children to take the name of the Lord in vain. Would you comment on that argument?"
This is when the lawyer noted it was really just a statement of political philosophy. As Newdow noted, this is a bit misleading given the context in 1954 [one brief eloquently argues it was intended as an illegitimate religious test oath] as well as the reasonable view of those who say the words today. Along with the danger of forgetting that noncustodial fathers should have the right to sue when their parent-child relationship is affected, it is a bit too easy to forget annoying atheistic zealots like Newdow alone aren't protected by the principles being argued. Defend a watered down "acknowledgment" of a religious entity, and many others are harmed as well.