It has to be a credible claim though, when we consider the increasing wingnuttery of Leibermann (suggesting Obama may be a Marxist, associating with John Hagee even after McCain rejected him), and the fact that most Americans just don't see the Democratic Party as being 'far-left' like Leibermann sees it. The party in general is more popular than it has been in a long time.
It will be much easier for Democrats to prove that Leibermann has changed rather than the other way. Remember the Republicans must have thought how great it was that Zell Miller was willing to speak out against the dems in 2004 and he ended up embarrassing them.
As regards my point, I think people are always automatically suspicious of someone who makes such an quick and major change in affiliation.