Roll Call reports Democrats also have been irked by Lieberman's opposition to President Barack Obama's jobs bill.
But Democrats, with whom Lieberman caucuses, have little recourse, holding only a slim majority of 53 Senate seats and with Lieberman retiring.
"Look, we have 53 Democrats in the Senate and need, at minimum, seven Republicans to join us to overcome incessant filibusters," a senior Democratic Senate aide said. "Regardless of how Senator Lieberman votes, the fact remains that we need Republican support to do anything and far too often we are left without it."
Roll Call says Democrats have been especially disturbed by Lieberman's recent discussions with Connecticut's 2010 Republican Senate nominee, former World Wrestling Entertainment Chief Executive Officer Linda McMahon, and his longtime friend, former Rep. Christopher Shays, a Republican, about their campaigns to win his seat in 2012.
Lieberman told Roll Call both Republicans had asked to talk to him and said he is willing to have similar discussions with Democratic candidates if they request them.
He offered no apology for meeting with the GOP candidates.
"My ultimate loyalty is to do what's right for the country. I don't mean that to be self-righteous; I just think that's what my job is," Lieberman said.
Lieberman said he's neutral in the Senate and presidential races but didn't rule out endorsing a GOP candidate in either. He says he's undecided on whether he will make any endorsements.
Notable deaths of 2014 [PHOTOS]