Clinton doesn't have any bases of support similar to that as the pro-Iraq War group has shriveled to nothing within the Democratic Party.
What about women? You don't think that even a few % of female Democratic primary voters would like to see Hillary elected, in the same way that Lieberman got support from Jewish Democrats? I'm sure that Hillary will get a much smaller %age of the women's vote than Lieberman got of the Jewish vote, but she doesn't need as much to match Lieberman's performance, since there are many more women than Jews.
And what about fans of Bill Clinton, some of whom will see a vote for Hillary as a vote for returning to the Clinton years? I know it sounds like a stupid reason to vote for someone, but there are a lot of voters out there who have a very unsophisticated understanding of politics.
There's also the fact that, because she's married to a former president, and because she's been regarded as the frontrunner for the nomination for the last two years, Hillary will get a lot more free press than Lieberman got in '03/'04. The media will still cover her even as her support erodes. On the flip side, Lieberman was never really considered the frontrunner by much of anyone last time around, even though he led most polls in early '03. Just like Giuliani this time around, most pundits were saying that he would never do well enough with the party's base to win the nomination.