As we wrote this morning, Barack Obama yesterday floated the idea that Virginia Governor Tim Kaine would be on his short list for a position in the administration. Convenient, given that Virginia holds its primaries today and given that Kaine is the most high-profile Democrat in the state who's chosen a candidate (Former Governor Mark Warner, running for Senate, has not backed a candidate, and neither has Senator Jim Webb).

Obama's public mullings about who would fill his cabinet and got us thinking, and the popularity of Veepstakes, over at the RCP Blog, got us wondering: Who would be a good fit for Obama, Hillary Clinton and John McCain? Today, we're offering the case for a few candidates for each contender in three different posts: Four real contenders, a long-shot hail Mary pick and one candidate to strike from the list.

We'll begin with the junior senator from Illinois, and that governor he was talking about:

Tim Kaine: Watch Virginia's voting pattern today. The incumbent governor, his predecessor and Webb have all won with huge margins in Northern Virginia's suburbs and exurbs, along with increasingly close contests in the state's southern third. If Democrats can tip Virginia toward their column, it will do a lot to getting the party back in the White House. John Kerry tried to woo North Carolina to his side by pulling John Edwards on board, a strategy that didn't work. Virginia is much closer to going blue than North Carolina, and picking Kaine could do the trick. Kaine is young, has management experience Obama lacks and can speak with a southern accent, which would help Obama at least keep the South close.

Kathleen Sebelius: The Kansas governor, like Kaine, helps Obama with management experience he lacks. Obama's outside-the-Beltway message would work well with a Midwestern Democrat elected in the reddest of red states, not once but twice, and he sort of owes her: Her endorsement, the day after the State of the Union, went a long way in advancing the storyline that Obama was starting to gain big-time red state backing, a great way to make the electability argument. And here's a bet to take odds on: If Obama picks Sebelius, she could even put her home state in play. That's not as crazy as it sounds; the Kansas Republican Party has long been split between conservatives like Sam Brownback and more moderate members like Pat Roberts and Bob Dole. Those moderates voted for Sebelius twice, and while they would most likely go with McCain, there's a chance for a big red state coup.

Claire McCaskill: After McCaskill's Obama endorsement, the two seemed attached at the hip. And while Obama won Sebelius' Kansas easily, he needed more help in McCaskill's Missouri, a state so close that several media outlets initially called it for Clinton before switching their projections. Missouri is a bellweather state, and a vice presidential nod could solidify its place in the Democratic camp this year. Plus, Obama the nominee will have just beaten Clinton, the first woman with a real shot at the White House, and he'll need to smooth some ruffled feathers with an important part of the Democratic base. As with Sebelius, picking McCaskill would go far toward healing those wounds. Don't forget, as well, that she was an auditor before winning the Senate seat. "When I was an auditor, stopping corruption in my home state," she could begin, feeding nicely into Obama's change message.

Jim Webb: Virginia's junior, and soon to be senior, Senator would, like Kaine, help move the state into the blue column. While Kaine brings managerial experience, Webb brings a military background, both as a member of the armed services and as former Secretary of the Navy, that both Democratic candidates lack. Webb fits the Obama message of bringing people together as well: A former Republican, he endorsed George Allen in 2000, then ran against him and beat him in 2006. A gun-toting ex-Marine former Republican Southerner would open a lot of new doors to Obama, probably as many, if not more so, than Kaine would.

Longshot: Mike Bloomberg: The billionaire Mayor, like Kaine and Sebelius, brings managerial experience to the table, and in a big way. Whether it's a Fortune 500 company he built himself or the largest city in America, he's been there, run that. And now that McCain looks like the GOP nominee, and assuming Obama wins the Democratic side, Bloomberg's hopes of swooping into the middle and attracting any votes for himself in the top spot have faded. The former Democrat-turned-Republican-turned-Independent doesn't add anything geographically, but he embodies competent management that remains a nice contrast with the Bush Administration. If Democrats keep hammering the notion that any Republican embodies a third term for President Bush, they're going to have to come up with someone who has made government work, and Bloomberg could be just that candidate.

Never Going To Be: John Edwards: The one-time vice presidential pick is old news. Obama wants his endorsement, and he wants Edwards' voters, but picking him for the number two spot brings too many negatives. Obama's argument that he was right the first time about Iraq is a powerful contrast with McCain, so why have someone on the ticket who voted the wrong way? In fact, why have someone who has apologized for a number of votes he took? Republicans are going to hammer Obama for lack of experience and, therefore, a lack of judgment. Picking Edwards only gives the GOP more fodder.

Check back in an hour for Hillary Clinton's veep possibilities.