Hensarling is expected to introduce his legislation shortly. Hensarling has been an outspoken critic of FSOC.

FSOC was created by Dodd-Frank and its duties include identifying risks and responding to emerging threats to financial stability. As chairman, the Treasury Secretary can call meetings and set its agenda.

The most controversial duty that FSOC now holds is designating certain financial institutions as "systematically important." In the most celebrated case, FSOC designated MetLife as systematically important, but the label was rescinded by a federal court.

FSOC includes the chairs of the financial regulatory agencies.

In one credit union-related action, FSOC has attempted to convince Congress to give the NCUA power over third-party vendors. That effort was supported by then-NCUA Chairman Rick Metsger, but was opposed by credit union trade groups.

More recently, NAFCU President/CEO B. Dan Berger asked Mnuchin to have FSOC use its power to review and place a stay on new rules issued by the CFPB.

Under Dodd-Frank, an FSOC member may petition the council to void a new CFPB rule that may "put the safety and soundness of the United States banking system or the stability of the financial system of the United States at risk."

The petition must be filed within 10 days of the rule's publication in the Federal Register and the petitioner must have attempted to address the concerns with the CFPB. Mnuchin would have the authority to place a stay on the rule until FSOC discusses it. It would take a two-thirds vote of the council to issue a further stay or to void the regulation.

Congress should make it easier for FSOC to place a stay on CFPB rules, Ryan Donovan, CUNA's chief advocacy officer, said.

"The FSOC should have an easier path to overturning regulations that present safety and soundness concerns to financial institutions or limit consumers' access to credit," he said.

He added, "If FSOC were reformed so that a majority vote could veto a rule, rather than a 2/3 majority, this could be beneficial to consumers to ensure that more voices are included in policymaking and to better account for safety and soundness concerns."

In a letter to Hensarling earlier this year, CUNA President/CEO Jim Nussle also called for legislation that would enhance FSOC's power over CFPB rules.

"The CFPB must provide more consideration about whether the burden associated with new rules is limiting the benefits credit unions are providing to consumers," he wrote.

In that same letter, Nussle said the Office of Management and Budget should be given power to review CFPB rules. The House recently passed legislation that would require federal agencies to submit their rules to OMB's Office of Information and Regulatory Affairs.

"These suggested changes would help ensure that CFPB rules do not impact safety and soundness of financial institutions and that consumer credit is not unnecessarily limited," Nussle wrote in his letter.

As Congress considers ways to roll back Dodd-Frank, credit unions should closely watch how legislation addresses FSOC, John McKechnie, senior partner at Total Spectrum and former chief federal lobbyist at CUNA, said. "Credit unions should pay very close attention" to whether Congress changes FSOC's power to place a stay on CFPB rules, he said.

Hensarling and others have been highly critical of FSOC.

In 2013, the GAO criticized FSOC for its lack of transparency.

The conservative Heritage Foundation also has been highly critical of the council.

"The Financial Stability Oversight Council was created based on the faulty premise that financial market deregulation caused the 2008 financial crisis," Norbert Michel, a financial regulations research fellow at Heritage, wrote in a report.

He said future government bailouts of financial institutions are likely because the agency identifies firms that financial regulators would consider catastrophic.

"The council also adds layers of complexity to an already tangled mess of financial regulations and seemingly absolves regulators of any responsibility for previous financial crises," he wrote.

Hensarling's committee staff last month issued a scathing report on FSOC. The report said that the council has failed to follow its own rules and that its analysis of companies has been inconsistent and arbitrary.

"The Obama Treasury Department tried to keep Congress and the American people in the dark about how FSOC exercises its sweeping powers," Hensarling said, as he released the report in a statement. "The release of this staff report brings some much-needed transparency and oversight to FSOC, and the information contained in the documents clearly demonstrates the need for the accountability reforms Republicans have proposed in the Financial CHOICE Act."