He’s not up for re-election until 2012, but according to a poll released Thursday, U.S. Sen. Joseph Lieberman may have a tough time if the anti-incumbent mood continues.

Lieberman, who became an Independent after he was defeated by Ned Lamont in the 2006 Democratic primary, would lose in a head-to-head match up against U.S. Rep. Chris Murphy according to the latest Public Policy Polling survey.

When stacked against Murphy as the Democratic candidate and two different Republicans, Lieberman fails to get more than 20 percent of the vote in a three-way or a third against just Murphy.

Head-to-head, Murphy leads Lieberman, 47-33, winning independents 41-33, pulling 70 percent of Democrats, and holding Lieberman to 59 percent of Republicans. If Peter Schiff enters the race Murphy gets 39 percent to Schiff’s 25 percent and Lieberman’s 19 percent.

The poll conducted Sept. 30 thru Oct. 2 found two-thirds of those likely to cast their ballots this fall are looking forward to voting Lieberman out of office in the next election—including 70 percent of Democrats, 61 percent of Republicans, and 63 percent of independents—while only a quarter are committed to re-electing him.

Outgoing Gov. M. Jodi Rell would be a stronger Republican candidate than Schiff, closing the Murphy advantage to 37-29 and bringing Lieberman down to 17 percent, the survey found.

Secretary of the State Susan Bysiewicz has also been mentioned as a contender in the 2012 election, but she was not included as part of the survey.

“Democrats, Republicans, and independents in Connecticut agree on one thing: they want Joe Lieberman replaced in the US Senate,” said Dean Debnam, president of Public Policy Polling. “His path to reelection, at least at this point a couple years away, looks extremely difficult.”

With a 31-57 job approval rating, Lieberman is tied with Ohio’s retiring George Voinovich for the fourth least popular of 60 senators Public Policy Polling has polled in 2010. That said, he is up significantly from the 25-67 mark measured in January.

As of August, Lieberman is still undecided about another run for the Senate. He has said he was going to wait until after the November election to make an announcement.