Brad,It is interesting that you should bring this up about the possibility of Barak having Jewish descent. His mother's maiden name of "Dunham" is definitely interesting. I am aquainted with a family with that name. Everything about them screams "Jewish". I read somewhere that this possibility of him being Jewish was raised. There are genetic tests you can take to determine if you are from Israeli descent. Immigration to Israel, I am told, is only allowed by extensive proof of lineage.
Also, this gentleman has some interesting theories on the lost ten tribes of Israel, and their whereabouts today.