But selecting a pick solely because he brings foreign policy heft could backfire, by conceding the Republican point that Obama needs shoring up on foreign policy, a deficit that could easily be addressed with any of those men named as Cabinet choices for the Departments of State and Defense.
And, more importantly, both the 69-year-old Nunn (or Biden) could well violate the one VP selection criteria prominently mentioned by top Obama campaign manager David Plouffe, who was quoted last month by The Atlantic's Marc Ambinder as saying, "We certainly don't want to pick someone who will hurt."
That criterion might exclude Nunn, who helped formulate the controversial military "Don't Ask, Don't Tell" policy when he chaired the Senate Armed Services Committee and engendered the enmity of the gay and lesbian community.
Similarly, former House Majority Leader Dick Gephardt, who ran for president in 2004 and gave Obama campaign manager David Plouffe a key job on his staff more than 15 years ago, could give the Illinois senator a big boost in the Midwest, but he became a Washington lobbyist since leaving Congress.
And that, by Plouffe's own criteria of do no harm, opens Gephardt up for the kind of client scrutiny that sank one of Obama's own vetting chiefs, former Fannie Mae official Jim Johnson, who had unfortunately gotten a sweetheart loan rate from mortgage lender Countrywide Financial.
In the "first do no harm" world, Joe Biden's reputation as a political loose cannon could stir concern, as well as reports that he plagiarized a British politician's stump speech during his own failed presidential run in 1988.
Although many modern presidents have come from the gubernatorial ranks, very few governors have been vice presidential candidates.
The Democrats have tapped members of Congress for running mates in 13 of the past 14 races. The only exception was George McGovern's choice of Kennedy in-law Sargent Shriver in 1972, but that was only after McGovern's first choice, Thomas Eagleton, withdrew. More about that later.
This year, with both candidates as sitting U.S. senators, governors may be looking more desirable as running mates than in past contests.
Obama could turn to Gov. Janet Napolitano, D-Ariz., or Sebelius, the daughter of a former -- and popular -- governor of Ohio, a Rust Belt state that has been in the camp of every winner of presidential contests in modern history.
But could Obama really choose a woman whose name isn't Hillary Rodham Clinton? On that point, some of the New York senator's closest advisers don't believe "Vice President Clinton" is in the cards.
Moreover, Plouffe -- and Obama himself -- have repeatedly made the point that geographical considerations aren't as important as they might seem. Plouffe pointed out that Al Gore didn't help Bill Clinton carry Tennessee in 1992, but Clinton won the presidency anyway.
In fact, most importantly, Obama and his aides have made clear that whoever joins the eventual ticket will have to share the candidate's vision of how to govern.
By that token, former North Carolina Sen. John Edwards might seem to fit the bill. He's had experience as a VP candidate -- but remember, Edwards' ticket-topper, John Kerry, lost North Carolina and didn't even win Edward's home precinct in 2004.
Other possible picks who share Obama's vision include Warner, a wildly popular politician and successful businessman -- but one who has firmly said he wants nothing to do with the "bucket of spit" and plans to run for the Senate. His successor, Tim Kaine, could fill the bill, as well, and his fortunes could rise now that Webb has taken himself out of the running.
Another VP pick who is looking attractive to many Democrats is Indiana's Bayh, who also spent two terms as governor of that Midwest state with its 11 electoral votes up for grabs. Bayh has plenty of positive attributes: He has executive experience, was a prominent Hillary Clinton backer, who would help bring along her supporters, could pass crucial vetting tests, and is unlikely to upstage the candidate.
The "upstaging" issue is not insignificant.
Lloyd Bentsen, for example, did Michael Dukakis no favors when he seemed so "presidential" that people started asking, "Why isn't this guy running for president?"
But the great unanswered question, as always, is "chemistry," though most historians agree John F. Kennedy and his running mate, Lyndon Johnson, were like oil and water -- and still proved a famously winning combination.
It's chemistry that is most likely to be the key factor in McCain's choice of a running mate, according to those who know the Arizona senator best.
"John McCain's running mate will have to be someone John McCain likes and is comfortable with," said one longtime adviser.
In other words, McCain will want someone who doesn't just help him on the stump but someone he can actually envision working with over the next four years.
That suggests he may see the office a little differently than he once did. Most of the GOP speculation to date has focused on McCain's one-time opponent, former Massachusetts Gov. Mitt Romney. Romney is said to be attractive because he is good on the stump, was a successful businessman -- which helps bring credibility to economic policies -- and can help bring in big-time fundraising dollars.
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