Does the president need to take the oath of office?
The timing questions are certainly interesting, but 1) If the JFK assassination isn’t an “extreme circumstance” I don’t know what is, but LBJ got sworn in promptly. 2) You don’t have to swear on the Bible for the oath to be effective, as it isn’t specified anywhere in the Constitution. 3) You can’t change the words of the Oath, as they are specified in the Constitution, Article II, Section 1, clause 8.
For (A), I see no reason you couldn’t take the oath with a single witness, so I don’t see any circumstances too extreme for that. Actually, I take this back. When Calvin Coolidge was sworn in after Harding’s death, it was by his father (who was a notary public). They re-swore him with a judge when they got back to Washington because they weren’t sure if it had been valid.
Arthur Schlesinger Jr. would appear to agree with Flunkie’s last point: “The oath required by the Constitution is preliminary to the ‘execution’ of the office, not to the holding of it. “The distinction between holding the Presidential office and discharging its ‘powers and duties’ is drawn in Article II, Section 1, two paragraphs before the stipulation of the oath. The taking of the Presidential oath is dramatic and symbolic, but supererogatory.
For (A), I see no reason you couldn’t take the oath with a single witness, so I don’t see any circumstances too extreme for that. Like valkyryn says, LBJ was sworn in by a handy federal judge. (The only woman to ever swear in a President, if you’re looking for trivia.) For (B), the Constitution just says “take the following Oath or Affirmation”. No Bible needed.