If I was going to bet on an out-of-the Bayh/Biden box pick, I'd vote Dick Lugar, the other, Republican, Senator from Indiana.
Of course, Obama always brings up their bi-partisan efforts to track down loose nukes, so the pick would weave perfectly into the Obama narrative.
They're clearly friends and that might be enough to get Lugar to turn on his party.
And he's everything Obama could ask for in terms of balance -- the anti-celebrity with off-the-charts national security cred, an open minded Republican white guy with middle-America written all over him.
His anti-abortion politics would be a hard swallow for the NARAL crowd, but the guy's not a firebreather on social issues.
For more, check out this NYT profile from 1995 when Lugar was a contender for the GOP nomination.