Not race, not gender, not backing from a large swing state with all its electoral votes - none of those attributes are as important for a vice presidential nominee as the ability to step up and take over as president, according to former Vice President Dick Cheney.

The former chief of staff to President Gerald Ford-turned-congressman from Wyoming-turned Defense secretary ran the vetting process for then-Gov. George W. Bush in 2000 out of the basement of his daughter's home.  But Bush ultimately settled on Cheney for the job of Vice President.

"What [George Bush] said to me after we finished the search and we'd reviewed all the candidates, he turned to me and he said, 'Dick, you're the solution to my problem,'" Cheney recalled today. "At that point, he basically put the arm on me and a few days later made the decision to sign me on."

Speaking publicly for just the second time since undergoing a heart-transplant last month, Cheney said it is important to remember that a presidential candidate's choice for a running mate "is the first presidential level decision you make," and it helps voters decide if the presidential candidate is up to the task of serving as president.

"I think the single most important criteria has to be the capacity to be president - that's why you pick them," Cheney said. "[The selection] gives the public a chance to see what you're like."

Cheney admitted that particular preference has not always been the standard in past selections, possibly a veiled reference to Sen. John McCain's choice during the 2008 campaign, when he selected former Alaska Governor Sarah Palin as his running mate, who was largely unknown and perceived by many as an ill-advised choice.

In his memoirs, Cheney wrote about his experience in helping select running mates.

"Sometimes the media refers to the 'long' list and the 'short' list, but it's really more like the list for public consumption and the real list of possible choices," Cheney wrote in 'In My Time.' "Perhaps you're trying to placate a certain wing of the party, or maybe you want to attract those who supported your opponent in the primaries. And so you mention certain people, although there's no chance they will be chosen."

Cheney, who was released from Fairfax Hospital  in Virginia on April 3, spoke for about 45 minutes to student interns at the Washington Center. He walked on and off the stage without assistance, appearing alert and engaged, although his voice seemed a bit scratchier than normal.