Rep. Chris Murphy (D-Conn.) holds a slight edge over former Connecticut Secretary of State Susan Bysiewicz for the Democratic nomination in the race for retiring Sen. Joe Lieberman's (D-Conn.) seat. 

Murphy leads Bysiewicz 40 percent to 38 percent, according to a survey from Democratic-leaning Public Policy Polling, which was commissioned by Daily Kos.

Another 21 percent of voters said they were undecided. 

The primary is a long way off, but Connecticut Democrats are anticipating a tough fight for the nomination with Murphy and Bysiewicz already sparring over early endorsements. 

Last week, four Democratic members of the state's Congressional delegation — Reps. Joe Courtney, Rosa DeLauro, Jim Himes and John Larson backed Murphy's bid for the nomination. 

Bysiewicz's camp called the endorsements a sign that Murphy is the Washington-establishment pick and highlighted her support from local elected officials across the state.    

The poll shows both Murphy and Bysiewicz easily besting Republican Linda McMahon in hypothetical general election match-ups. But against former Rep. Rob Simmons (R-Conn.), both Democrats are less than 50 percent with a much larger pool of undecided voters. 

Neither McMahon nor Simmons have made an official decision on a 2012 run, but both are considering bids.