"We are not opposed to arbitration," said John McElligot, deputy executive director of the Commissioned Officers Association. "We are opposed to forced arbitration."

The supporters said that the exact timing of the vote is uncertain since Senate Republicans on Tuesday decided not to consider the Obamacare overhaul since they did not have the votes for it.

They said that the Senate could move to a vote as soon as Wednesday, but added that it remains uncertain whether Republicans have the votes to pass it.

The CFPB rule prohibits financial institutions from using arbitration agreements to keep consumers from being part of a class action suit. Immediately after its release, congressional Republicans announced their intentions to try to nullify the rule.

Using the Congressional Review Act, House Republicans passed a resolution to nullify the rule. The resolution is pending in the Senate, where, if it is brought to the floor, it cannot be filibustered.

Credit union officials have been pushing the Senate to consider the resolution since they oppose the rule. They have said that few credit unions use arbitration and that their institutions should be exempt from the regulation.

Saunders criticized Senate Republicans for pushing the resolution a week before officials from Wells Fargo and Equifax are scheduled to testify before congressional committees.

She said the two organizations are "poster children" for why mandatory arbitration clauses should be prohibited.