Senate Majority Leader Harry Reid (D-Nev.) sent strong signals Sunday morning that he wants Sen. Joe Lieberman (ID-Conn.) to remain in the Democratic fold, but he said his fellow Senate Democrats will determine Lieberman’s future as chairman of the Homeland Security and Governmental Affairs Committee.

“The Caucus has a decision to make and they’re going to make it. I am not going to make the decision,” Reid said in an interview on CNN’s Late Edition. He said the question before the Democrats is, “Whether we’re going to say, ‘OK, we’ve had enough of you, Joe, go vote with the Republicans’ or whether we’re going to try to work something out with Joe Lieberman. Say, ‘Joe, we don’t like what you did. And here is what we propose we’re going to do.’”

Senate Democrats might vote on Lieberman’s fate at their next regular policy luncheon on Nov. 18. Senators will be in town for a brief, lame-duck session.

Reid had strong words for Lieberman’s decision not only to endorse Republican presidential nominee Sen. John McCain (Ariz.), but also to aggressively criticize the candidacy of President-elect Obama. Lieberman had told fellow Democrats he would not do the latter, but broke that pledge, most publicly during his speech at the Republican National Convention in early September.

“Joe Lieberman has done something that I think was improper, wrong, and … if we weren’t on television, I’d use a stronger word of describing what he did,” said Reid.

Still, Reid, who has been friends with Lieberman for years, said his Connecticut colleague does not belong in the Republican Party. GOP Senate leaders have been actively courting Lieberman in recent days, and they have said they would warmly embrace him as one of their own.

“Joe Lieberman is not some right-wing nut case,” said Reid. “Joe Lieberman is one of the most progressive people ever to come from the State of Connecticut.”

Reid credited Lieberman with sticking with Democrats on almost all crucial votes outside of those issues related to the Iraq war, and Reid said he would not have been Senate majority leader for the past two years if Lieberman had not opted to continue caucusing with Democrats after winning re-election in as an Independent. Lieberman lost his Democratic primary in 2006 largely because of his outspoken support for the Iraq war.

Reid met with Lieberman on Thursday to discuss his role in the next Congress, most particularly his position on the Homeland Security panel. During that session, Reid reportedly told Lieberman he would not continue as that committee’s chairman in the 111th Congress, and instead offered up several lower-profile committee chairmanships. Although neither Senator has revealed those options, Reid made clear Sunday that he has not offered Lieberman the chairmanship of the Senate Veterans’ Affairs Committee.

“He’s not on the Veterans’ committee. I couldn’t offer it to him if I wanted to,” said Reid. Still, Reid did not dispute that he had offered Lieberman the chairmanship of another “lesser committee” in exchange for Lieberman relinquishing the gavel at Homeland Security. Lieberman does sit on the Armed Services; Environment and Public Works; and Small Business and Entrepreneurship committees.