By no means do I claim any job of the Holy Spirit, but the Bible does say "you will know them by their fruit." Supporting or attending the National Day of Prayer doesn't make one a Christian, giving their life over to Jesus does. For this reason I do not stand in judgment (the eternal kind) of Barack Obama.
I can and in fact I have Biblical authority to make some decisions by the spiritual fruit he produces. The Bible also has this nugget that I use as fruit inspection. Jesus said in Matthew 10:32-33 "Whosoever therefore shall confess me before men, him will I confess also before my Father which is in heaven. But whosoever shall deny me before men, him will I also deny before my Father which is in heaven."
To celebrate a National Day of Prayer by sitting in the back room and signing a proclamation is very telling.