The Issue is Bush
At least that's the preliminary conclusion I derive from this exit poll analysis by Glenn Greenwald:
2) Apparently, a more significant factor than the Iraq war was opposition to President Bush generally. Fifty-nine percent of all voters said that Lieberman "was too close to the President," and although no exact numbers are provided, it was that group which "voted overwhelmingly for Lamont." The most reliable factor in the Lamont win seems to have been not opposition to the war specifically, but a more generalized disapproval of President Bush and of Lieberman's support for the president.
Greenwald points out that, according to this exit poll, 40% of anti-Iraq-War Connecticut Dems still voted for Lieberman. So opposition to the Iraq War is not the defining issue of this campaign. It is opposition to Bush in general that is the key to this election.
The American people are tired of Bush but Bush cannot be removed (barring an unlikely impeachment). So what the people want are representatives who will at least work to check Bush's outrageous actions.
It's not simply a matter of running against Bush. It's running for the principle of oversight that will bring in the votes.