Early on, there were people who thought the Dunhams must have been Jewish, but then the whole Muslim thing overwhelmed that.
His half-brother Mark Obama (whom he never sees) is or considers himself Jewish.
Michelle's first cousin is Rabbi Capers Funnye, chief Rabbi at Ethiopian synagogue in Chicago which is about a century old. You'll occasionally see them referred to as "Black Hebrews", but it's not an odd denomination, he's an ordained Rabbi and they're probably somewhere around Modern Orthodox. They did have him to the White House in 2009, but what can you do with a prominent Jewish cousin GWB had to the White House. I've read they have little to do with him, and have the impression he's not a democrat. Which is the real issue.