There's been a lot of moralizing about the holdout strategies of Lieberman and Nelson, but under some game-theoretic accounts it is a blessing in disguise, a blessing for Obama at least. For instance Rahm Emanuel can now say to the House: "look, we just can't renegotiate this any more or the coalition will fall apart. You'd better get on board with the Senate version of the bill" A lot of these legislative games don't otherwise have a core, or it takes so long to find the core that the deal falls apart in the meantime.
The holdout behavior of one decisive Senator decreases the need to cut bargains with other members of Congress. The key words here are "credible precommitment to no further renegotiation." The more anxious or wavering Nelson and Lieberman were/are, the more credible this precommitment.
Often it's easier to trade with one or two guys than to suffer death by a thousand cuts by having to appease the larger group, yet again. Keep in mind that Obama probably needs this bill more than do most of the Democrats in the House, so he can't just stonewall and win the staredown. In addition to his other roles and effects, Lieberman arguably serves as Obama's "bad cop" enforcer.