From an AP article
According to Mark Tushnet, a constitutional law professor at Georgetown University Law Center, it is possible for Bill Clinton to become vice-president.
The 22nd Amendment to the Constitution imposes a two-term limit on presiden-tial candidates, but imposes no limit on the vice presidency. As vice president, however, Clinton could succeed the president upon death, incapacity, impeach-ment or resignation and serve a third term.
That leads to the 12th Amendment, which states that “no person constitutionally ineligible to the office of president shall be eligible to that of Vice President of the United States.”
Is the 22nd Amendment an “eligibility” requirement? Arguably not, says Tushnet. Article II of the Constitution defines who is eligible to be president as a natural born citizen, at least 35 years old, who has been a U.S. resident for at least 14 years. It says nothing about term limits.
But others might argue that permitting Clinton to run for vice president violates the spirit of the 22nd Amendment. The issue ultimately would be decided by the U.S. Supreme Court, which in 2000 resolved the disputed presidential election in President Bush’s favor.