Since the United States constitution had nothing to say about traitor I went to the Dictionary to see if it would help us decide whether or not Barack Obama is a traitor.
Definition: Traitor (Noun)
1. a person who betrays another, a cause, or any trust.
2. a person who commits treason by betraying his or her country.
Well by definition 1 certainly a traitor he's obviously against what his oath guarantees he will protect.
But definition number 2 is obviously more applicable so I had to look up treason.
Definition: Treason (noun)
1. the offense of acting to overthrow one's government or to harm or kill its sovereign.
2. a violation of allegiance to one's sovereign or to one's state.
3. the betrayal of a trust or confidence; breach of faith; treachery.
Since he is probably the closest to it's sovereign lets rule that one out.
It's obviously treason by 3, betrayal of a trust of confidence or dare a say: "solemn oath", and then again violation of allegiance and violation of oath of office seem to be pretty synonymous, so I'd say treason by number 2 as well.