Bill sponsor Rep. Roger Williams (R-Texas) said that the CFPB has not exercised its authority to exempt small institutions from its rules. His legislation would allow the CFPB to ask banking regulators for permission to waive the exemption if bureau officials believe it is warranted.

“One size, believe it or not, does not and should not, fit all,” he added.

Williams accused the CFPB of “bureaucratic over-reach.”

But Waters said the legislation would weaken oversight of financial institutions, adding that former CFPB Director Richard Cordray did exercise the exemption authority.

NAFCU and CUNA supported the legislation.

“If the CFPB is unwilling to tailor its rules using its existing authority, Congress should require it to do so through this legislation,” CUNA President/CEO Jim Nussle said in a letter to the committee.

But it might be difficult to get the bill through the Senate, where Democratic supporters of the CFPB could move to block it.

The bill was one of 15 bills approved by the committee. The House already has passed Financial Services Chairman Jeb Hensarling's (R-Texas) Financial CHOICE Act, would overhaul the Dodd-Frank Act.

The Senate is not expected to consider Hensarling's bill. Instead, Senate Banking Chairman Mike Crapo (R-Id.) and a bipartisan group of senators have crafted a more modest regulatory overhaul bill.

Waters said that several of the bills approved by the Financial Services Committee were part of Hensarling's bill and were included in the Senate bill.

She called the measures “misguided,” adding that they would weaken important components of Dodd-Frank.

During the markup, the committee also approved H.R. 4607, which would require financial regulators, including the CFPB and the NCUA to review all regulations once every five years.