"We just believe it creates an environment for more sensible rulemaking from collaboration, much like among this committee, from different minds," Murray, chairman of the Nevada Credit Union League, told Brown during a Senate Banking Committee hearing. "When you have one person in charge of the entire bureau, who sets that agenda? One person essentially. We just feel like it's a more common sense approach to coming out with common sense regulation."

Neugebauer said his bill is not an attempt to weaken the CFPB.

"It is a push to strengthen the CFPB and ensure greater consumer protections for the American people. I look forward to working with my colleagues on the Financial Services Committee and in Congress to move this much-needed bill forward," he said.

CUNA and NAFCU, along with other financial trade association, wrote a letter of support for the legislation, which currently has 20 co-sponsors.

"We believe that a five-member commission, as Congress originally intended, will better balance consumer access to financial products with the need to ensure a fair marketplace," the letter, addressed to Neugebauer, said. "A commission would serve as a source of balance and stability for consumers and the financial services industry by encouraging internal debate and deliberation, ultimately leading to increased transparency."

Neugebauer, the current chair of the House Financial Services financial institutions and consumer credit subcommittee, is scheduled to speak at CUNA's 2015 Governmental Affairs Conference on Monday.

The ABA, the American Financial Services Association, the Consumer Bankers Association, the Financial Services Roundtable, the Independent Community Bankers of America and the U.S. Chamber of Commerce also signed the letter.