LAST LINE OF THE TEXT OF 12th AMENDMENT
"But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
Obama is not eligible to be president as he has served two terms (22nd amendment). Therefore, he is not eligible to be vice president.
Obama vp is still possible. You forget the MOHAP
That’s why Q post 4083 is pointing to this article: The Hill article from post 4083