Biden: 'I am not running' for the papacy

Truthfully, Biden would have been a long shot for the papacy. The last pope elected from outside the College of Cardinals was Pope Urban VI in 1378, and the last person selected who was not already an ordained priest or monk was Pope Leo X in 1513.

But the Vatican opening is also somewhat unprecedented. When Pope Benedict XVI announced Monday morning he was resigning, he became the first pontiff to do so in 598 years.

New York Cardinal Timothy Dolan, who has received some more realistic attention as a papal candidate, told CBS News that Church officials would likely look for a credible and compelling public speaker for their next head.

"I think Catholics in general and certainly the College of Cardinals would look for a man who’s able to articulate the truths of the faith … in a compelling way – in a compelling, credible way – a man of deep piety, a man who knows the church universal and the needs of the people throughout the world," Dolan said.