Sen. Joe Lieberman, D-Conn., has lost some support because of his backing of the Iraq war, but 64% of voters in his state believe he should be re-elected, a Quinnipiac University poll found.

The poll found 24% opposed his re-election and the rest didn't know. Lieberman, the 2000 vice presidential nominee and running mate of Al Gore, is seeking a fourth Senate term in November.