Schumer said Neugebauer, a longtime critic of the CFPB, would not be acceptable as a replacement. He contended that as chairman of the House Financial Institutions subcommittee, Neugebauer was a defender of the payday loan industry.

“That's like putting the biggest arsonist in the firehouse,” he said.

Warren said the CFPB is working on rules governing arbitration agreements, payday loans and debt collection. She accused businesses involved with those activities of actively lobbying for Cordray's removal.

The senators said that converting the agency into a five-member commission would not be acceptable to Democrats.

Two Republican Sens.—Ben Hasse of Nebraska and Mike Lee of Utah—have called on Trump to fire Cordray. However, Senate Banking Chairman Mike Crapo (R-Id.) declined to support that effort, simply saying that Cordray should quit so Trump can appoint his own director.

To make matters even more uncertain, Trump's ability to simply fire Cordray is hung up in federal court.

Currently, Cordray may only be fired for cause, Warren said, adding that no federal agency head has been removed for cause for more than a century.

A panel of the U.S. Circuit Court of Appeals for the District of Columbia ruled that the structure of the agency is unconstitutional since it is governed by a single director who can only be removed for cause. The panel said that the president has the power to fire the director for any reason, but has stayed its order.

The ruling came in a case in which PHH, a mortgage lender, was the subject of $109 million penalty from the CFPB. A panel of appellate court judges voided that penalty and sent the case back to a lower court for review.

The CFPB and the Obama Administration have asked that the full D.C. Circuit Court of Appeals consider the case.

And last week, the appellate court gave PHH until Jan. 27 to file a supplemental brief—effectively ensuring that there will not be a ruling before Trump takes office.

Brown said that Trump voters supported the President-elect because they believe the financial system is unfair.

“The people who voted for Trump believe the system was rigged,” he said, adding that Trump should support Cordray who, he added, has been fighting that system.