A bill backed by House Republicans that would replace President Obama's financial regulatory law is headed to the House floor after the Memorial Day break, according to the House calendar.

The legislative package, authored by Financial Services Committee Chairman Jeb Hensarling of Texas, would cut back many of the rules created by the 2010 Dodd-Frank reform law and limit the power of regulators. The centerpiece of the plan, the Financial CHOICE Act, is to offer banks the option of avoiding many of the new rules if they choose to maintain a higher level of capital.

Additionally, the legislation would dramatically curb the power of the Consumer Financial Protection Bureau and reform the Federal Reserve's regulatory and monetary powers.

The version of the bill that the House will vote on will not include one provision that pitted the banking industry against retailers and other merchants; a repeal of a limit on debit card fees that was passed as part of Dodd-Frank.

That provision, the Durbin Amendment, complicated the bill's path to passage in the House as some Republicans sought to avoid casting a difficult vote amid intense lobbying by retailers, grocers, restaurants and other industries that benefit from paying lower fees on debit card transactions. The legislative package initially cleared the committee earlier this month.

Michael Needham, the CEO of the conservative advocacy group Heritage Action, said that it was "disturbing" that some Republicans would support "price controls" on card fees, but said nevertheless that his group would back passage of the legislation. "Rolling back significant parts of Dodd-Frank remains a priority for conservatives and is essential for U.S. economic growth," he said.

Retailer and grocers, however, praised leadership for taking the Durbin Amendment repeal out of the bill.

The Financial CHOICE Act, H.R. 10, is not expected to be taken up in the Senate, where Republicans must strategize around a potential Democratic filibuster.

Nevertheless, Republicans have expressed hope that certain provisions within the larger bill could pass the Senate, such as the reforms to the CFPB.