I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States.
You may have noticed that Supreme Court Chief Justice John Roberts said “So help me God” at the end (and Obama repeated after him). But that’s not part of the official of the oath, is it?
No, and in 2008, Michael Newdow filed a lawsuit (PDF) to prevent exactly this scenario from taking place:
Defendant Roberts… will (with no authority whatsoever) alter the text of that document to infuse the inaugural ceremony with purely religious dogma.
Newdow also laid out the history of those four little words. Basically, no president said the words “So help me God” until “1881, ninety-two years after George Washington’s initial ceremony” — when “Chester A. Arthur took the oath upon hearing of President James Garfield’s death.” After that it didn’t become a “tradition” as we know it until 1933 (with Franklin Roosevelt). In short, there was no reason to continue this “tradition.”
His lawsuit was later thrown out, but Roberts’ own counsel said in a 2009 response to the lawsuit (PDF) that there was nothing wrong with the phrase and that the Chief Justice said “So Help Me God” not as an official part of the oath, but as something the President wanted him to say “after the conclusion of the constitutional oath.”
So it was just a personal request by the President (similar to his request to swearing the oath on a pair of Bibles), not Roberts circumventing the Constitution. That’s the story and they’re sticking to it.
Though when you watch that video, there’s no noticeable difference between the official and “unofficial” parts of the oath…