Except for Constitutionally described procedures, the Senate is free to make its own rules. Why not kill the current bill, it is an abomination by now anyway and change the rules of the Senate to allow cloture at 51 votes instead of 60. If I understand correctly this change could be made with a simple majority vote in the Senate. Once this change is made, introduce the HCR bill in its original form again needing only 51 votes to get it to the floor. Lieberman becomes irrelevant. 51 votes to amend, 51 votes for passage. Sounds like Democracy, doesn't it.
The best part....
Lieberman standing there wondering who had fucked him.
Some aide whispers in his ear it was the Liberal DKOS fanatics that dreamed it up.
Joe has a stroke and lives out the rest of his life in a coma in a government facility.
I know this is an idle fantasy, but it made me feel better. :)