[Verginius Rufus]

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 could become Acting President if he became Speaker of the House and the President and Vice President were both removed, killed, or decided to resign without time for a new Vice President to be chosen. That's not going to happen.

[JosephW]

He is constitutionally eligible to be president, but not constitutionally eligible to be elected president.

22nd keeps him from being elected
He could be VP to a president that resigns.

He is sleepy enough.