Hawkish Democrats Say “No!”
In a brilliant move, the Republicans are declining to endorse Connecticut’s Republican senatorial candidate Alan Schlesinger, but according to White House press secretary Tony Snow, are instead endorsing “the democratic process” in CT generally.  Since it can be safely assumed that the President of the U.S. of A. would publicly support “the democratic process” even when he has a preference of candidates, this endorsement only of Connecticut’s general “democratic process” without a stated candidate preference is clearly a signal to Republicans that voting for Lieberman is fine by him, even preferable. The Republican National Committe is doing the same.
Now, no one can fault the Republicans for seeking to divide and conquer their opponents. 
And certainly, there are plenty of reasons for hawkish Democrats to be concerned with their party’s continually troublesome far-Left flank.   
But Lieberman is not our hero.  Even beyond his support of Bush in this war, he has been problematic.  Not because of the reasons the far-Left offered, but because of why TNR says so.

He has supported capital-gains tax cuts, ultra-loose financial regulations and the crucial vote on the grotesque bankruptcy bill. He has an almost pathological need to be liked by the far right.
Above all, he has maddeningly failed to acknowledge just how badly the Iraq war has turned out, which is different from insisting that we have to fix the mess we created. After all, many hawkish Democrats such as Senator Joe Biden of Delaware supported the war and don’t want to retreat but fully acknowledge President Bush’s catastrophic management of the occupation.
Lieberman’s persona has therefore tainted his admirable foreign policy instincts with his un-admirable domestic and political ones […]Still, the Lieberman rationale held together, just barely, as long as he was fighting the good fight within the Democratic Party. But now that he’s running as an independent, the last pillars of that rationale have crumbled. 

Even for hawkish Democrats, Lieberman has long been suspect.  But now, by dismissing (inexplicably, even before the primary took place) the wishes of Democratic voters, he has turned into our greatest foe, as he is currently the most powerful advocate that there is no place for us in the Democratic Party.
He no longer deserves our support. 
Now he deserves our full wrath.