CBS News anchor Katie Couric reports the guessing game has already started, but the process usually takes months, with a behind-the-scenes dealer heading up the search.
Every candidate appoints someone to help with the vice presidential selection process.
That individual's role, said former Ronald Reagan chief of staff Ken Duberstein, is to act as "the Sherpa, the guide. The Sherpa lays out what I refer to as the four tests for any potential vice president: Competence, chemistry, credibility and compatibility,"
In addition to assessing the "four Cs," the person in charge of the search is also in charge of the vetting.
"The first consideration is to find a candidate who won't do you any harm," said former Senate majority leader George Mitchell.
You could call that the Hippocratic Oath.
"Who won't hinder your chances to win and then of course, who can best help," Mitchell said.
With McCain's age a factor - and national security experience a given - he might seek help from someone with a different resume.
"...he needs somebody who matches John McCain's proficiency in foreign policy and national security on the domestic side," Duberstein said.
And although we won't know the pick for some time, the dealing has already begun.
Some Senate wildcards like Kay Bailey Hutchison, R-Texas, have been thrown into the mix.
One thing's clear: McCain's pick could be a revealing look into his leadership style.
"The vice presidential pick is absolutely critical for what it tells you about a presidential candidate's ability to make sound judgments," Duberstein said.
Geography mattered for FDR, who had three vice presidents for his four terms.
"It used to be said FDR would pick a different VP every four years - many of them unknown simply because he wanted to win a state," said presidential historian Douglas Brinkley.
Party unity was paramount for centrist Dwight Eisenhower when he tapped conservative Richard Nixon.
"He never liked Nixon," Brinkley said. "They weren't compatible, but he needed him and stuck with him two times because it got the 'hard right' off his back."
In the case of Bill Clinton and Al Gore in 1992, two similar candidates made for a winning pair.
"They both came from the same region," Brinkley said. "They both were young, but the combination of their youth and energy, attractiveness politically at the time … it was a huge positive factor."
In 2000, it was the man in charge of George W. Bush's search who ended up taking the prize.
And sometimes, bitter rivals in the primaries become critical allies in the general election.
"Without Lyndon Johnson being picked as V.P., John Kennedy probably wouldn't have been able to win," Brinkley said.
Duberstein said: "I happen to think George Herbert Walker Bush helped strengthen Ronald Reagan."
Some are still hoping it could happen with the two current Democratic contenders, though it looks less likely every day.
What about the notion of a Clinton/Obama ticket or an Obama/Clinton ticket?
"I think it would have a great deal of appeal," Mitchell said. "If Democrats feel that the two of them together would be the best ticket and one of them declines for personal reasons, that will have an effect on his or her own future in the party."
But other names are already being drawn.
For Obama, national security chops like Jim Webb's or Gen. Anthony Zinni's, or executive experience like Mike Bloomberg's might strengthen his hand.
For Clinton, a big swing-state governor like Ohio's Ted Strickland or Pennsylvania's Ed Rendell could appeal.
Or even ... Mitchell himself.
"I would suggest that a George Mitchell makes an awful lot of sense because of his gravitas, because of his international experience," Duberstein said.
Couric asked Mitchell: "Is the vice presidency anything that you would ever consider?"
"I think given all the circumstances, there's about as much of a chance of my being vice presidential candidate as you being chosen by Sen. McCain," he laughed.