Kraninger would replace Acting Director Mick Mulvaney, who has been running the agency even as he continues to serve as director of the Office of Management and Budget.

"Credit unions look forward to working with a new, permanent…Director, one that we hope will recognize the unique structure of credit unions and the enormous benefit credit unions provide to American consumers in need of financial services," Nussle wrote.

But Nussle and NAFCU President/CEO B. Dan Berger have said the single-director structure of the CFPB should be replaced by a multi-member commission.

"Only through the appointment of a bipartisan commission will the Bureau have the type of independence that proponents herald and the steady approach to regulation that consumers and regulated entities need," Nussle wrote in his letter. "We appreciate that legislation has been introduced in both chambers and encourage Congress to address this fatal flaw and look forward to working with you on this matter."

And earlier this year, Berger said, "We still believe the best path forward is to eventually establish a bipartisan commission at the bureau to ensure its decision making is as fair and transparent as possible."

While the credit union trade groups support Kraninger, Democrats and consumer groups oppose the nominee, who has said she agrees with Mulvaney's decisions.

"Since taking control of the CFPB last year, however, Mick Mulvaney has undermined the CFPB's important mission and turned an organization meant to stand on the side of the American people into yet another outlet for the financial industry to push its agenda," Senate Banking ranking Democrat Sherrod Brown of Ohio said, in a report issued this week. "Mr. Mulvaney has undermined the Bureau's mission at nearly every turn, and President Trump's pick to succeed him, Kathy Kraninger, has refused to repudiate any of Mr. Mulvaney's actions."

Meanwhile, Seth Frotman, who resigned earlier this year as CFPB student loan ombudsman as a protest against Mulvaney's leadership on Wednesday announced the formation of a new group, the Student Borrower Protect Center.

The group, which includes former CFPB employees, plans to work with organizations on student lending issues.