I'd bet a lot of money that Lieberman won't lose, assuming a serious candidate can be found to run against him in the first place. Moveon.org would find better use for their money running candidates against moderate Republicans like Chris Shays and Jodi Rell.
I think that George Soros will give them as much money as they need to go after whoever they want. However, I have a feeling the left will see Lieberman's support of Bush as a monumental betrayal and will try to make him suffer for it.