Jesus existence has nothing to do with the religion in and of itself. He can be reall without Christianity being true. You’re getting so caught up in wanting to argue against the theists that you’re focusing on something completely irrelevant just to chalk up a victory.
I have no evidence one way or another for our against his existence, the point is that it doesn’t matter. Jesus’ potential existence has nothing to do with the truthiness of religion unless you believe that his existence can only be a validation of the new testament - which would be akin to your Obama comparison and would be patently ridiculous.
I have no proof that billions of specific people existed, doesn’t change that they did.