Or could they? Some Constitutional scholars have argued it's possible. Columbia University law professor Michael Dorf explored the topic in 2000, when the exiting Bill Clinton was being earmarked as a running mate for Al Gore. Clinton, Dorf argued, wasn’t “ineligible,” just not electable—a big difference. If a former-president-turned-veep were to re-take office, it wouldn’t be due to an election, it would be due to the departing president’s death, removal, or resignation. The same would hold true for serving more than two terms—the third would be a succession, not an election.
A 2006 Washington Post article delved into the question further, finding three lawyers and a federal judge who agreed—with Hillary Clinton eyeing the Oval Office, they asserted that nothing in the Constitution would prohibit a two-Clinton ticket (the issue of them being from the same state is a discussion for another time). Others, however, stated taking “elected” at face value is being too literal, and that the spirit of the amendment was to prevent anyone from holding office for more than two terms regardless of how they arrived there.
The latter argument was supported by Bill Clinton, who has been fielding questions of his possible vice presidency alongside Hillary. Talking to David Letterman in 2007, Clinton said that “I just don’t believe it’s consistent with the spirit of the Constitution for someone who’s been president twice to be elected vice president … I don’t think it’s right and I wouldn’t want to do that.”
Grilled by Mario Lopez in 2015, Hillary Clinton echoed the sentiment, saying that her husband is “not eligible … it would not be possible for him to ever succeed to the position.”
An equal amount of confusion existed back in 1960, when Dwight Eisenhower jokingly floated the idea of running for vice president. He didn't, of course, for the same reason few presidents have ever sought office after stepping down: after ruling the free world, no one wants to accept a demotion.
