In the suit, filed in the U.S. District Court for the Northern District of Texas, the groups contend that the structure of the CFPB is unconstitutional.

That argument also is pending before the U.S. Court of Appeals for the District of Columbia, where a mortgage company has argued that the agency’s makeup is unconstitutional since the director may only be removed for cause.

In the Texas suit, the business groups also contend that the rule violates the Administrative Procedures Act because the CFPB relied on a flawed study in issuing the rule.

The groups allege that the CFPB failed to take into account problems that the rule poses, saying that it is the “very model of arbitrary and capricious agency action.”

Finally, the groups argue that the rule fails to advance the public interest or consumer welfare.

“If the rule goes into effect, it will inflict immediate, irreparable injury on Plaintiffs,” the groups argue. “Providers of consumer financial products and services will incur significant legal and compliance costs in adapting their businesses to the new rule; the vast majority of these costs will be wasted, and not recoverable, if the Rule ultimately is deemed to be contrary to law.”

A CFPB spokesman declined comment on the suit.

Credit unions have been pressing the Senate to follow the House in using the Congressional Review Act to nullify the rule. Congress can nullify agency rules by passing a resolution within 60 legislative days of the agency action.

Consumer groups said last week that they feared that a Senate vote on the resolution was imminent.

However, the Senate did not consider the legislation last week amid speculation that supporters of the resolution did not have the 50 votes needed to pass it.