OK, I wasn't there and I may be faulty in recollection about Lieberman's support from the National Democrat resources. I do KNOW that Clinton campaigned for him in the Primary and I will take your word about Obama. My recollection is that the rest of the support was quite luke-warm and diminished rapidly as the Primary went on and Move-On and its ilk made such waves for Lamont.
Well, it varied. The left wing of the Dem Party was pretty luke-warm, whereas other Dems pretty actively supported Lieberman. But I think there's a pretty stark divide between "luke-warm support" and open betrayal. Open betrayal would be the Dem Nat Committee actively recruiting candidates to run against Lieberman. That's not what happened.