Reid needs 60 votes (let's put aside reconciliation for a moment). He announced yesterday that he doesn't have 60 votes. That makes the last couple of votes very valuable. If there are only 60 possibilities, then Reid is in a jam. However if there is even one Republican considering voting for cloture, Reid can play this to his advantage.
Let's suppose that there are 58 votes for cloture and Lincoln, Lieberman, and Snowe have not committed to support cloture. Then, the 59th vote is valuable, the 60th vote is very valuable and the 61st is worthless. A smart majority leader will negotiate with each of these three senators separately (and if Collins is in play, well that makes it easier).
He will make clear that the first two Senators to join will get something very valuable (or avoid some pernicious punishment like being thrown out of the caucus). However he will also make clear that the third Senator to commit will get nothing (or will receive some pernicious punishment by getting thrown out of the caucus).
If Reid has the brains to play it right (and I don't know if he does) then the real competition is between the waverers. Seen in that light Lieberman is using a public forum to try and get as much as he can for his vote. He wants his vote to be harder to get than any Democrat. He probably thinks Snowe won't vote for a trigger-less bill and so he can maximize his asking price.
Reid should spend much of the next few days with Snowe and any other potential cloture voters and shut out Lieberman. If Reid can give the public impression that he can get cloture without Lieberman, Lieberman will come around. This is not a trivial task but even a statement that Snowe or Collins might consider cloture may do the trick.
Lieberman is bargaining in public here. Reid has to undercut his position by making credible threats and more importantly making Lieberman think he's unnecessary.