I don't believe that ClintonCare was ever up for a vote in either chamber of Congress, despite the fact that the Dems then controlled both houses.
The filibuster was at the very end, as Danforth and some other RINOs were trying to ‘cut a deal’ with the Dems. Dole, thankfully, was still able to get 41 of the 44 Republicans on board to keep it from being voted on. I think they filibustered by talking it to death, since they had the votes to block it. I remember the end-game vividly, it was damn close.