Upon two germane bills going to conference, the House and Senate choose their members. The whole House has complete discretion over its selection of members. The Senate normally lets the leadership choose conferees, but there is a motion that allows for the Senate to select conferees in toto. This motion is divisible and may be debated according to the traditional rules of the Senate, which means that there has to be a cloture fight again. It would require one defector to the GOP side, but it may be possible (check Lieberman, Nelson).
Before each of you comment, I know that this procedural move is difficult to implement, but I just wanted to make all of you aware of one of the methods available to us before we throw our hands up in lamentations.
There is a strong possibility to kill this bill in conference since the House Democrats are severely fragmented. The goal of the Senate selection motion would be to stack the conference committee with so-called "moderates" who could pick a fight with the statists in the House.
Feel free to add other ideas to slow/stop this monstrosity as they come to mind.
Does each party get to pick which of its members are on the reconciliation committee? Does Pelosi get to say which Republicans, or the Republican leaders in the House?