Appear with a candidate: The VP buzz begins

(CNN) -- It is vice presidential season, where every picture looks like a campaign brochure and introductions sound like tryouts.

Few know what's going on, and everybody gets asked about it.

"This is a very personal decision for Sen. Obama, and I have no inside information as to how he is proceeding with this decision," Sen. Hillary Clinton said Wednesday of Barack Obama, the presumptive Democratic nominee for president.

Clinton lost her Obama vice presidential buzz weeks ago. Last week it swirled around Virginia Gov. Tim Kaine, who brings both demographic and geographic elements to the table, is a devout Roman Catholic and a moderate Democrat who might help pull his Southern state into the Democratic column.

Kaine escorted Michelle Obama to a Virginia fund-raiser this evening, brushing aside vice presidential inquiries.

"You know, I'm not running for anything. My highest and best use is trying to be a good governor and trying to help Sen. Obama in Virginia," Kaine told CNN's Wolf Blitzer Thursday. Watch more of Kaine's interview »

Hundreds of miles to the west in Elkhart, Indiana, Sen. Evan Bayh and Sen. Obama were looking chummy co-campaigning, and there was an Obama ad team crew shooting video of Bayh at the event.

So the question becomes: What does the vice president want?

There are knowing -- or unknowing -- smiles in response. A former governor and a current senator, Bayh is a Midwest moderate and a platinum name in Indiana, a Republican stronghold.

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"Well, I would like to think that kind of thing wouldn't hurt his chances," Bayh said Thursday.

It could be either Bayh, or Kaine, or neither of them. Also in play: former policy power player and Delaware Sen. Joe Biden, and the well-credentialed governor of New Mexico, Bill Richardson.

It is showtime on the Republican side too. Former Massachusetts Gov. Mitt Romney has been sporting his abilities in the role frequently left to number twos, attack dog.

With deep political roots in Michigan, Romney is geographically well-suited to help presumptive GOP candidate Sen. John McCain. A former governor, and a hugely successful CEO, Romney's economic prowess would also complement McCain's foreign policy credits. Predict the future vice presidential candidates

Minnesota Gov. Tim Pawlenty sparred with reporters Thursday. He is energetic and innovative with a Washington-free resume. Pawlenty could take some of the same-old/same-old feel off the Republican ticket, counterbalancing McCain's age and decades in Congress with a light touch. Watch Pawlenty speak to reporters Wednesday »

When asked what the most important qualities in a vice presidential candidate are, Pawlenty said: "Discretion."

There is truth in humor. They are all like that, these vice presidential maybes, skirting, flirting, trying not to seem eager, while still being available.

CNN political producer Ed Hornick contributed to this report.

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