12th Amendment, in part says:
“But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States.’
So much for “Plan C”.
The left will say that the qualifications under the 12th amendment are simply “be a natural-born citizen, at least thirty-five years of age, and a resident of the United States for at least fourteen years”.
I think it’s most likely that SCOTUS would see pushing Obama into the VP slot as a blatant attempt to circumvent the 22nd Amendment. Even a strict textualist like the late Justice Scalia would have seen through it. Still, I would expect a 6-3 or possibly 5-4 ruling.