In practical terms it does. The average voter, and swing voters in particular blame the party in power for whatever happens. They gave power to the Pubs, and they hold the party in power responsible for anything bad that happens. The Pubs can no longer blame anyone but themselves. That's political reality.
If 100% Dem opposition and 5% GOP defections give the Republican Party full ownership, then that is just a simple matter of PR incompetence.
Let the bill fail; the people will continue feeling the pain. Spin it the right way, and the Dems get the blame. GOP should pick up more House and Senate seats next year.