The 22nd amendment clearly says No person shall be elected to the office of the President more than twice.
There are no further qualifiers that change this prohibition.
Obama cannot serve a third term. No one can have a third term.
The best that can possibly occur is if a Vice President succeeds a President for less than two years, then runs for election and wins. He can have one more election so the most that could be served would be 2 1/2 terms.
Lyndon Johnson was the only one of which I can think who might have been able to do this. It's very unlikely this will ever be possible again.