Inaugural

Obama begins, "I, Barack Hussein Obama, do solemnly swear ... "  That starts the door swinging shut; the latch is slid home when he reaches the period at the end of the sentence.

(One aspect of my work requires "certifying", and I've actually had to research what is sufficient in order to argue that a particular document we had should be accepted as a written certification.  I also do a lot of swearing at work.  )

The earliest known source indicating Washington added "So help me God" to his acceptance, not to the oath, is attributed to Washington Irving, aged six at the time of the inauguration, and first appears 65 years after the event.[8] Even if Irving's report is accurate, it would not by logic, law or intent alter the actual words of the oath, being more accurately described as a personal prayer by the President after completing the oath of office.

The only contemporary account that repeats the oath in full, a report from the French consul, Comte de Moustier, states only the constitutional oath.[9], without reference to Washington's adding "So Help Me God" to his acceptance.

Evidence is lacking to support the claim that Presidents between Washington and Abraham Lincoln used the phrase "So help me God." A contemporaneous newspaper account of Lincoln's 1865 inauguration states that Lincoln appended the phrase "So help me God" to the oath.[10] This newspaper report is followed by another account, provided later in the same year after Lincoln's death (April 15, 1865), that Lincoln said "So help me God" during his oath.[11] The evidence pertaining to the 1865 inauguration is much stronger than that pertaining to Lincoln's 1861 use of the phrase. Several sources claim that Lincoln said "So help me God" at his 1861 inauguration, yet these sources were not contemporaneous to the event.[12][13] Shortly after giving the speech, Lincoln stated that his oath was "registered in Heaven."[14], something some have taken as indicating he likely uttered the phrase "So help me God." Conversely, there was a claim made by A.M. Milligan (a radical Presbyterian minister who wanted the U.S. government to be officially Christian) that letters were sent to Abraham Lincoln asking him to swear to God during his inaugurations, and Lincoln allegedly wrote back saying that "God's name was not in the Constitution, and he could not depart from the letter of that instrument."[15] [16]

Other than the president of the U.S., many politicians (including Jefferson Davis, sworn in as president of the Confederate States of America in 1861) used the phrase "So help me God" when taking their oaths.[17] Likewise, all federal judges and executive officers were required as early as 1789 by statute to include the phrase unless they affirmed, in which case the phrase must be omitted.[18]

Since FDR, all presidents have added the phrase "So help me God."

A do-over "would take him 30 seconds, he can do it in private, it's not a big deal, and he ought to do it just to be safe," said Boston University constitutional scholar and Supreme Court watcher Jack Beermann. "It's an open question whether he's president until he takes the proper oath."

Section 1. The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.

Before he enter on the execution of his office, he shall take the following oath or affirmation:--"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."

The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.

3. If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.