GOP bill would undo health law's auto-enroll provision

"Many small-business owners have told me they are scared by the high cost of complying with the Affordable Care Act," Pittenger said in a statement.

"Repealing this provision of Obamacare will provide businesses with more confidence to grow."

U.S. retailers quickly backed the bill along with the restaurant industry, which said auto-enroll would lead to "financial hardship" and "confusion."

Angelo Amador, a vice president with the National Restaurant Association, pointed to young people employed in food service who often shift jobs or receive insurance through their parents.

"Many are likely to inadvertently miss opt-out deadlines … causing significant, unexpected financial hardship when they learn their paycheck has been reduced to cover the new premium," Amador said in a statement.

Auto-enroll's supporters say an opt-out system benefits consumers who might otherwise go without insurance, which will make them liable for penalties starting next year.