The Politico offers this breaking news report, “Lieberman Says War Vote Could Prompt Party Switch.” A switch, as the article notes, would give control of the Senate to Republicans. UPDATE: Political Insider reports: “Lieberman Switch Wouldn’t Flip Senate.”
UPDATE 2: Over on the Legislation listserv, Dan Lowenstein writes (reprinted with permission):

The point of the Political Insider article is that the Senate organizing resolution adopted at the beginning of the current Congress says the Democrats will retain control for the entire Congress, whereas the resolution adopted at the beginning of the 107th Congress (2001) had no such provision. That is an important point, very much worth pointing out. But it is not necessarily decisive.
The reason is that the Senate is so vulnerable to delaying tactics that it must operate on some sort of consensual basis. If Lieberman were to vote with the Republicans (I have no idea if that is likely), the Republicans could demand a switch of control. The difference in the organizing resolution would strengthen the Democrats’ bargaining position, but that is about all. Some sort of compromise, such as each party having equal membership on committees, might be likely, but who can say how it would be worked out?
There is a different reason why “Jeffords II” is an inappropriate name for the situation if Lieberman joins the Republicans, though I expect the name will stick. Jeffords was elected as a Republican. His withdrawal of his organizing vote from the Republicans so as to flip control of the Senate was contrary to precedent and in my opinion quite improper. The same would apply (except that it would no longer be contrary to precedent) if Lieberman had been elected to the Senate as a Democrat. Since the Democrats in their wisdom declined to nominate him in 2006 and he was elected as an Independent, there would be no basis for criticizing him for caucusing with whichever party he likes.

Greg Magarian has followed up with a post (link not yet available) stating that Sen. Lieberman promised to caucus with the Democrats, and that he would be breaking that promise to caucus with the Republicans.