Well, now it appears that Senator Byron Dorgan (D-ND) has said that Lieberman’s behavior is unacceptable for a committee head:

As a chairman of one of our significant committees in the Senate, not just going off and supporting a presidential candidate of the other side but also criticizing the candidate on our side, and also involving himself in a couple of senate races on the other side. The question is, is that acceptable? The answer is no.

I think the thing that may tip the Senate is his campaigning for Republicans in Senate races.

While the only two Senators to explicitly call for his removal as chairman of the Homeland Security Committee, Dorgan, from North Fracking Dakota, comes pretty close to it.