Lieberman said he was “inclined to let the motion to proceed” (or cloture) go forward, but “I haven’t decided yet.”I don't think that's what he's saying, although the Register's syntax here is almost impossible to parse. The next sentence, I think (although I'm not sure) clarifies it a bit:
He said he and others would attempt to negotiate changes in the bill before there is a filibuster.Remember, there are multiple filibuster points on any piece of legislation. If I had to guess, what Lieberman is saying here is that he intends to vote cloture on the motion to proceed (which gets the bill to the floor), but he's not committing at all to voting for cloture on the final debate over the bill.
Moreover, I think it's fairly likely at this point that Republicans are not going to attempt to keep the bill from being considered. A better plan for them is a death-by-amendment strategy, in which they always have just a few more amendments to offer, and they can portray their eventual vote against cloture as a defense of procedural fairness (because they still have amendments to offer), rather than as a flat-out attempt to kill the bill. That pose attempts to entice Democrats (Nelson, Lincoln, Lieberman) by allowing them to kill the bill (by opposing cloture) without actually opposing the bill.
If I had to bet, I'd bet that Democrats are going to hang together and that the bill will eventually pass with 61, 62, or 63 votes -- I think Ezra's right about where Holy Joe winds up. But the specific quote hints only that the battle isn't going to come on the motion to proceed.