"The 12th Amendment is lengthy, and provides a lot of important information, regarding the election process of the president and vice president. The most important line, in regards to our viewer's question, is as follows:That sums it up nicely."No person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States,” it reads."
Leaving aside for the moment the question of whether or not Obama is a natural born citizen - there are only three eligibility criteria.
1) NBC
2) Lived in the US for the last 14 years
3) Be 35 years old, or older.
Almost every answer to my vanity begs the question by saying, if you can’t be ELECTED President after 6.1/8/10 years as POTUS, that makes you “ineligible to SERVE as President”, since there are several ways to become President besides being elected.