A CRA challenge takes only 51 votes to pass in the Senate—unlike much legislation, which requires 60 votes to pass in the polarized Senate.

Congress must act within 60 days on a resolution filed under the CRA.

Until this year, the process was only used successfully once, but this year, Republicans have used it several times.

The CFPB is under fire from congressional Republicans, as well as the Office of the Comptroller of the Currency

Under the CFPB rule, companies still can include arbitration clauses in their contracts, but they may not use those clauses to stop consumers from being part of a class action lawsuit. The rule specifies the language that must be used in the contract.

The rule also requires companies to submit to the CFPB detailed information about claims and awards made in arbitration—data that eventually will be made public.

Cotton said the rule will not help consumers—only class action attorneys.

He said that every Republican member of the Senate Banking Committee will cosponsor a resolution to nullify it.

"At least a few Democrats realize the need to reverse this rule," he added.

Meanwhile, Acting Comptroller of the Currency Keith Noreiga also has threatened to take the rule to the Financial Stability Oversight Council, which also may void CFPB rules. He said he is concerned that the rule will affect the safety and soundness of the banking system.

However, Senate Banking Committee ranking Democrat Sherrod Brown of Ohio charged in a Tuesday letter that Noreiga has other motives.

"Previously, as an attorney in private practice, you represented Wells Fargo in just such a case, and attempted to quash a class action brought by consumers harmed in exactly the same way by invoking Wells Fargo's forced arbitration clause," he wrote to Noreiga. "Indeed, Wells Fargo is one of the entities for which you were subject to a conflict of interest recusal until May 18th of this year." 

Brown asked Noreiga to provide background information to him before he files a petition under the FSOC process.

He said that the OCC had plenty of time to object to the rule, but only did so after the CFPB said the final rule would be published. He asked Noriega for all communication between the agencies discussing the rule.

Depending on how quickly the confirmation process takes, Noreiga may not be in office to finish the job, since the Senate is beginning the confirmation process for his permanent replacement.