Party officials say the group plans to get input from the town officials and revisit the issue in December.
"If you have someone who says they're a Democrat, who is registered as a Democrat and is a national figure supporting a candidate who is opposed to all the ideals and beliefs and positions that we hold as Democrats, he's diluting, in my opinion, the meaning of our party," said Audrey Blondin, a 30-year party veteran, before the meeting.
Lieberman was re-elected to the Senate as an independent after losing the Democratic primary in 2006 to businessman Ned Lamont. While he calls himself an "independent Democrat" in the Senate, he remains a registered Democrat and has said he has no plans to change his party affiliation.
Lieberman was the Democratic nominee for vice president in 2000 and ran for the party's presidential nomination in 2004.
Lieberman and independent Sen. Bernie Sanders of Vermont have been caucusing with Democrats in Washington, giving the party control of the Senate with what is effectively a 51-49 majority - even though each party has 49 members. Democrats, in turn, have made Lieberman chairman of the Homeland Security and Governmental Affairs Committee.
Blondin said Lieberman's speech at the Republican National Convention, in which he praised McCain and criticized Democrat Barack Obama, convinced her that state Democrats need to take a stand.
"Our point is not that Joe should in some way be prohibited from supporting McCain or speaking at the National Republican Convention. That's not the issue," Blondin said. "The issue is, he's a Democrat. And Joe, in our opinion, needs to reconsider membership in our party."
Lieberman, speaking earlier Wednesday to a radio station, said that he was surprised by the move to censure him.
"Honestly, I thought that was the kind of thing that happened only in the former Soviet Union. I understand that people are unhappy, but, you know, I'm doing something that I really believe," Lieberman told WICH-AM. "I thought in this country you don't get punished for that. So, I hope that in the end, my colleagues will understand and life will go on either way."
