I agree that Lieberman is an acceptable voice from the left. However, I have a theory that he would have been handicapped in a national campaign due to his vague resemblance to Max Wright. :)
http://www.tvshows.de/alf/e-cast2.htm#max
Max was the bumbling character from "Alf".
Senator Hubert Humphrey also had a similar albatross hung around his neck when he ran for President. He bore a striking resemblance to a movie and TV start who invariably played a relentless villain.
But I think Lieberman looks more like Dick Cavett.