Lieberman, who ran as the vice presidential nominee on Al Gore's unsuccessful ticket in 2000, told Fox Business Network on Thursday that he hopes Representative Alexandria Cortez-Ocasio (D-N.Y.) doesn't think she's the future of the Democratic Party.
Ocascio-Cortez previously responded to Lieberman's statement, writing on Twitter, "New party, who dis?".
Ocasio-Cortez has been very vocal on social media and unafraid of criticizing members of her own party.
They also quoted Democrats, such as Rep. Emanuel Cleaver (D-Mo.) saying things like this: "I'm sure Ms. Cortez means well, but there's nearly an outstanding rule: Don't attack your own people".
Now, Democratic members of Congress are saying they're done with her "sniping" at their own party and aren't sure if her career in Congress will go too well if she keeps up the criticism.
House Democrats were also annoyed that Ocasio-Cortez sought a seat on the powerful Ways and Means Committee - on which veteran lawmakers typically serve - with a grassroots campaign to pressure Speaker Nancy Pelosi to add her to the panel, Politico reported, adding that Ocasio-Cortez's office denied being behind the effort.More news: Fed's Powell Again Stresses Patience as US Economy's ‘Narrative' Unfolds
"I'm sure Ms. Cortez means well, but there's nearly an outstanding rule: Don't attack your own people", Rep. Emanuel Cleaver (D-MO) said.
"She needs to decide: Does she want to be an effective legislator or just continue being a Twitter star?" said an anonymous House Democrat in the Politico report, who said he agrees with her radical ideology.
Some lawmakers are trying to convince Ocasio-Cortez to use her influence to unite Democrats, while others have warned her that she's headed for a lonely tenure in Congress if she treats her more moderate colleagues as enemies, the report said. "She doesn't understand how the place works yet".
A spokesman for the campaign told the New York Daily News that the campaign had nothing to say.
'If you look at the majority of new Democrats in the House, ' he said, 'they tend to be - I say, center-left. and that is because they had to be center-left to win some of those competitive swing districts that they took from Republicans'.
Instead, the open downstate NY slot on the House Ways and Means Committee went to a moderate Democrat, Long Island Rep. Tom Suozzi, a former CPA, attorney and county executive.