Already been tried.
In that thread there was a serious concern that the security measures involved to get the president in and out would really hurt the event. So although I really want this to happen, it's just not feasible.
Here's an idea: maybe he gives a live speech from at the white house to be displayed during opening ceremonies/reward ceremonies/whenever. Less of a burden on him and its logistically possible.
Also, if you want FIRST people to sign a petition, July isn't the best time to do it.