Steve Schmidt, a senior strategist to McCain's 2008 presidential run, said campaigns are "very careful to have a very inclusive list of people" as potential running mates to avoid giving offense.
Last month, when word surfaced that Rubio wasn't being vetted, it could have created considerable grief for Romney in Florida and with Hispanics. Romney quickly came out and said that Rubio was being "thoroughly vetted."
More often, though, Romney clams up when asked about his search efforts.
That's a far cry from the vice presidential selection process of earlier decades, when candidates were paraded before cameras and, ultimately, very publicly ruled out, causing considerable embarrassment. Walter Mondale, the Democratic nominee in 1984, would fly potential running mates to Minnesota for interviews and hold joint news conferences.
More recently, candidates have gone to great lengths to keep their deliberations secret until they're ready to announce a choice.
When George W. Bush settled on Dick Cheney in 2000 more than a week before his running mate was to be announced, aides worried the secret might not hold. Campaign architect Karl Rove's solution: lie.
Rove told a campaign aide who was known to leak information to reporters: "Don't tell anybody — but it's going to be Danforth."
That evening, three networks reported that former Sen. John Danforth of Missouri had emerged as a top candidate for the GOP ticket.
"We'd gotten what we needed: a little breathing room for Cheney's announcement," Rove wrote in his memoir.
Too much secrecy, though, can prove problematic, particularly when a vice presidential choice is not well known.
George H.W. Bush's surprise announcement at the GOP convention in 1988 that he had selected Sen. Dan Quayle of Indiana quickly overshadowed Bush himself when questions surfaced about Quayle's service in the National Guard during Vietnam.
"Within hours, it was attracting all the ink and TV time we had counted on for George's official rollout as nominee," James Baker, Bush's campaign chairman, wrote in his memoir.
Light said leaking names of serious contenders gives campaigns an opportunity to see what unsavory issues might be dredged up by interest groups and the press, and to find out whether the questions will peter out or mushroom. He likens it to entering a horse in lower-profile races before the Kentucky Derby.
"You want to see how your horse does under real conditions against strong competitors," Light said.
Romney promises to reveal his decision on a running mate before the GOP convention in late August but won't share much more.
When his wife was asked by CBS last week if she had a favorite candidate, she said: "I like to think that I have a few that I really like a lot."
Romney himself would add just three words: "What she said."
Associated Press writer Kasie Hunt contributed to this report.
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