Sen. Chris Murphy (D-CT) - May encounter accusations of inexperience and criticism for being only a one term Senator - though he'll have served as much time in the Senate as Barack Obama when he was elected. He's young and may prove to be a political force in time.
As a liberal Democrat from Connecticut, I promise you that Murphy would be a joke of a pick. Murphy sucks; he represents all the bad aspects of the Democratic Party and few of the good. He was clearly the lesser of two evils in a race against the horrendous Linda McMahon, but most CT Democrats found themselves wishing that someone like Himes (CT-4 representative) had stepped up and voted for Murphy with little enthusiasm. He also won by 12 points in a state that Obama won by 22 points. 12 points is still a big win, but it means he is a below average candidate, whereas Obama was an above average candidate (Gore, an average candidate, won by 17 points).
Also, it is very unlikely that Clinton will pick someone from New England on her ticket, and it would be impractical if she did. Clinton has appeal in the Northeast and the South; her ideal VP pick would be from either the Midwest or the West.
