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.
That will stop him from trying to steer from behind with Michelle ( AKA Big Mike )
But IF Big Mike were to get in at any level, that automatically includes the kenyan. I could see them trying to do it. There is no rule or law that they give even a glancing concern about.