good post. That's a tough one. I know I don't live down there but still I think I can comment. I haven't voted yet since I really don't know. I understand that 1) US is almost a melting pot, so whatever the majority are religiously(in the faith that believes in "god"
that is what goes sorta(this sentence was written horribly, i hope to edit it) 2) With diversity comes required changes, recently in Canada they were considering allowing family laws from arab states to be allowed in family court ruling because of the number of arab people in Canada. This has been denied so far as there was protests to its validity in modern civilization(some of the laws are discriminatory to women). There is a name for these laws just atm it escapes me, will edit.
Personally I am an athiest with spiritual beliefs. God has no meaning to me personally. We have the word God in our national anthem as well and well it doesn't make me uncomfortable to say it but at the same time my opinion says it doesn't need to be there.
I think if this was to be put into place to do this would require a national referendum, thing is the majority might just leave it there since they are well...the majority.
Now God can have many faces though too, they may call him "Alah", or other names but it is also God to them, just not the Christian view of God. So again for these people it might not be offensive to recite this as they can just think of their God when doing so.
There is that stigma though that it means the Christian God and noone else. There could also be a harsh backlash if they removed it from the religious sector as just another political correctness "destroying the base of which this country was founded"...so again really tough one, great post.