Obama's jokes about his origins and name weren't "self-deprecating". They were merely symptomatic of his true evasiveness on his subject and bordering on the weird.
Obama showed little sense of humor, although he felt he had to try because of the venue. Humor and playful humility are not in his arsenal. He is a wooden egotist and it shows. My wife thought he had an evil and insincere smile and she's pretty good at reading people.
Your wife is right. Hussein does have an evil and insincere smile, and that's because he's an evil and insincere man. But one thing he is sincere about is his determination to remake America into the socialist, authoritarian "paradise" that he has advocated ever since his rise to political prominence in Chicago's corrupt Democrat machine.