According to the source, McConnell approached Senate Majority Leader Harry Reid (D-NV) Monday night saying he was prepared to accept the deal that passed last night. This was a deal Boehner wasn't a party to and reportedly didn't really like, but McConnell's assent basically locked it in -- if Boehner didn't go along the story would have turned into one about the division between McConnell (whose caucus is relatively disciplined) and Boehner (whose caucus is anything but).
All of which is to say, as Steny Hoyer did on Twitter Tuesday morning, "McConnell said: This entire fire drill was completely unnecessary. He is right. What he didn't say is GOP House leadership made this happen."