Here I'll weigh in. Working with groups like Public Knowledge and EFF in killing SOPA, we were going to lose the Senate on PIPA until the President weighed in. We heard from Senate staffers who felt there was an arrangement between the parties until the President (through IP staffer Victoria Espinal) put out his statement.
The White House letter, as murky and contradictory as it was, represented a clear break with its previous unequivocal support for the MPAA/RIAA position.