Vice President still has to meet the qualifications to be president. If Obama were to run as Biden's VP with the plan that Biden serves 2 years plus 1 day and then resigns, Obama would still not be qualified because he already served two complete terms.
-PJ
That's true, but the 22nd Amendment isn't exactly a model of clarity. It says that no person shall be
elected to the office of President more that twice, not that no person shall serve as President for more than two terms.
There is a straight-faced argument, I think, that a former two-term President could run as a Vice-President, and that would be OK under the 12th Amendment.