Obama cannot be VP.
There's actually no law preventing this according to my political science professor.
A two term President being elected Vice President would most definitely be contested, given the rules established by the 12th, 22nd and 25th amendments. The 12th amendment makes it clear that no person who is not qualified to be President can be Vice President. In other words, all requirements that apply to the Presidency also applies to the Vice Presidency.
The 22nd amendment says no one can be President or Acting President for more than 10 years, or be re-elected if their next term would allow them to sit out more than 10 years. And the 25th amendment makes it clear that upon removal of the President from office, the Vice President becomes the President.
While some argue that the 12th amendment deals with service, whereas the 22nd amendment deals with elections, I am not sure that argument would stand in the US Supreme Court. It is quite clear that the framers of the 22nd and 25th amendments meant for the same restrictions to apply to the Vice President, but given the 12th amendment's language didn't see the need to include that explicitly.
But we will probably never know, as the issue is unlikely to actually occur. Due to these amendments, no one will actually attempt it. So in practical terms, my statement still stands.