Despite the calls for Cordray's ouster, it remains unclear whether Trump has the power to simply fire him at will. That issue is tied up in federal court, where a panel of appellate court judges has said that the organization of the CFPB is unconstitutional since it is governed by a single director who only can be fired for cause.

However, that ruling has been stayed, as the Circuit Court of Appeals for the District of Columbia decides whether to go along with a request by the CFPB to have the entire D.C. appeals court decide the case.

Democratic supporters of the agency have warned that the firing of Cordray would result in a lengthy legal battle.

Meanwhile Federal Trade Commission Acting Chairman Maureen K. Ohlhausen announced today that she has appointed Thomas Pahl, an advocate of deregulation as Acting Director of the FTC's Bureau of Consumer Protection.

Pahl is a partner at the Washington, D.C. law firm of Arnall Golden Gregor.

Pahl is a former FTC official, who also served as managing counsel in the CFPB's Office of Regulations.

In a recent interview with Bloomberg BNA, Pahl predicted big changes at the CFPB.

“I think there's going to be a change in the senior leadership of the CFPB very soon, and with that change in leadership there will be a greater opportunity to raise concerns with the agency about costs and unintended consequences of its policy choices, especially when it involves newer technologies,” he told the news service.