Sen. Ted Cruz has made killing the Consumer Financial Protection Bureau one of his key stances on banking policy during his fight to become the Republican presidential nominee.

Some argue that a President Cruz—or any Republican victor—could attempt to argue that CFPB Director Richard Cordray should be removed "for cause" before his term ends in 2018. While the provision has rarely been invoked and the cause would have to rise above Cordray's political leanings, some say there's enough room for Cruz to act.

Alan Kaplinsky, chair of the consumer financial services group at Ballard Spahr, said, "I don't think either the current president or President Cruz, if he becomes president, is ever going to have sufficient grounds for removing him."