According to "Rasmussen Reports", this is not the case. The poll that they have taken shows that he only has a 5% advantage in a three way race. Not a great percentage for a well know senator who did not have to campaign in his state in 2000 to win his third term.

Connecticut Senate: Two Days After Primary,- August 12, 2006
Lieberman Ahead by 5
Lieberman 46%, Lamont 41%

Survey of 500 Likely Voters
August 9-10, 2006
Election 2006: Connecticut Senate
Joseph Lieberman (I) 46%
Ned Lamont (D) 41%
Alan Schlesinger (R) 6%

Senator Joe Lieberman’s decision to run as an Independent sets up a lively campaign season for Connecticut voters. In the first General Election poll since Ned Lamont defeated Lieberman in Tuesday’s primary, the incumbent is hanging on to a five percentage point lead. Lieberman earns support from 46% of Connecticut voters while Lamont is the choice of 41%

If you look at the broader picture that would indicate that lieberman would get about 40% of the 30% of CT voters who are democrats (12% of all voters). Lamont gets the other 60% of democratic voters (18% of all CT voters).

The quinnipiac poll shows the general election split as 51% Lieberman, 27% Lamont and 9% Schlesinger (the repulican candidate). This would mean that Schlesinger is pulling less than half the republican vote which the other half is not likely to go to Lamont. So going into the decisive group, the independents, Lieberman has 33% of the vote (12% from democrats and 11% from republicans) and Lamont has 18% of the votes (all from democrats). Maybe there is 1% of the total vote that is republican in CT and would vote for Lamont, but I seriously doubt it.

So if the independents break 1 out of 3 for Lieberman (aka 2 out of 3 votes for Lamont), Lieberman still wins (at least as the race looks now). Since the independent vote is not likely to be more left leaning than the CT democratic vote, it is more likely that the independents will at worst split 50-50 and at best follow the democratic 60-40 split.

Add into this that Lamont in June Lamont had a double digit lead that fizzled to a 4% lead and you can see that the polling arc for Lamont looks like he peaked already.

An internal party movement that can narrowly defeat an opponent in the primary but is not likely to win in the general election is not a sign of strength for that party.

A great point about the Lieberman situation from Ken McCracken in the comments: JFK would be a Republican today... JFK ran on tax cuts, strenghtening missile defense and prosecuting the Cold War (including building up our presence in Vietnam). Think......