It's actually happened. Via Bloomberg:
The U.S. Senate advanced Richard Cordray's nomination to lead the Consumer Financial Protection Bureau under a compromise announced by Majority Leader Harry Reid, who said officials were working on final details.U.S. Senate Majority Leader Harry
Reid, a Democrat from Nevada, said he thinks "everyone will be happy"
with the compromise on confirmation votes for the seven presidential
The vote today was 71-29,
with 60 needed to advance the nomination. Senators will debate the
matter for as many as eight hours and hold a final confirmation vote.