From Peter to Francis: A Biblically Misguided Route

The resignation of Pope Benedict XVI and the election of Argentine Cardinal Jorge Mario Bergoglio to replace him brings up, once again, the Roman Catholic claim that the pope is the successor of the apostle Peter as the head of the church of Jesus Christ here on earth. To the Catholic, Francis now sits on Peter's throne.
The first question to be determined, of course, is: Did Peter have a throne? If he really was the early church's proto-pope, then it's reasonable to assume he had a throne—or at least something like it. And if he left a successor, who in turn left a successor and so on, then I suppose it's reasonable to say Francis is now the throne's rightful owner. This is the first question to consider since the mere fact of the office's existence deserves to be examined in light of the Word of God. After all, Catholics and Protestants take Scripture to be authoritative and infallible. A concept with such incredible import, then, must have some kind of biblical foundation. But does it?