ABC News’ Jan Crawford Greenburg and Howard L. Rosenberg report: Since he arrived back in Washington D.C. early Monday, Sen. Barack Obama has spent hours with the co-chairs of his vice presidential committee search team — Caroline Kennedy and attorney Eric Holder. On Monday night, Kennedy was the draw to a $1,000-a-head Georgetown fundraiser and today, rumors are swirling, thanks to an anonymously sourced Washington Post story, that Obama has settled on Virginia’s Democratic Gov. Tim Kaine. But all of Obama’s potential "short list" names have their own shortcomings. Let’s start with the flavor of the day: Kaine. Kaine and Obama have forged a friendship since Kaine became the first governor outside of Illinois to endorse the Senator. They share family roots in Kansas and Harvard law degrees. Yet, though Kaine is firmly on Obama’s shortlist of potential running mates, the 50-year-old Catholic has his own deficits. He is a liberal-leaning Democrat from a mid-sized, conservative swing state who won election to the statehouse only three years ago. Before that he was mayor of Richmond, a mid-sized, insular Southern city that prides itself on having been the capital of the Confederacy. He has no foreign policy or defense experience, a credential deficit for which Obama has been criticized too. And he is virtually unknown on the national stage. The other top contenders — Indiana Sen. Evan Bayh, Delaware Sen. Joe Biden and New York Sen. Hillary Clinton — are all sitting senators. But picking Bayh could complicate Democratic plans to try and win a 60-vote cloture-proof majority in the Senate. If an Obama – Bayh ticket won in November, there’s a chance a Republican governor could replace Bayh in the Senate. In Indiana, the statehouse is contested. If a Republican wins, he would take office before Bayh is inaugurated. In Delaware, Sen. Joe Biden has a Senate seat for life if he wants it, and he could shore up Obama’s own foreign policy shortcomings anyway as Secretary of State. The governor of Delaware, Ruth Ann Minner, is a Democrat, so his seat would stay on that side of the aisle if he gets the V.P. nod. But some Democrats worry he can be a loose cannon — and are concerned his selection could also concede the point that Obama, in fact, needs a senior VP with foreign policy experience to shore him up. Most observers believe that Obama’s statement on NBC’s Meet the Press Sunday that Sen. Clinton “would be on anybody’s short list” of VP candidates was just a sop to her constituency. And complicating the equation in the senate of course is the 2000 Democratic vice presidential candidate, Connecticut Sen. Joe Lieberman who now calls himself an Independent Democrat and caucuses with the party. But if Lieberman speaks at the Republican Convention as rumored, staffers in the senate say the Democrats plan to strip him of his chairmanship of the Homeland Security and Governmental Affairs Committee, kick him out of the party caucus and he will, for all intents and purposes, become a Republican.