Supporters of the bill from both parties praised it as a way to avoid having to mail out millions of notices to customers each year that simply remind people of their current privacy policy. In a separate statement Monday, the National Association of Federal Credit Unions praised the bill for allowing banks to avoid what they say is an unnecessary and costly notification.

"Such disclosures must take place when a customer relationship is first established and annually in paper form as long as the relationship continues even if no changes have occurred," the group said. "This legislation would help eliminate the confusion by providing some exemptions from this outdated requirement for institutions whose policies have not changed."

But senior members of the House Energy & Commerce Committee said during floor debate that they oppose the bill and that banks should continue to provide these notices even when there are no changes. Rep. Edward MarkeyEdward (Ed) John MarkeyDemocrats protest Trump's immigration policy from Senate floor Dems press EPA nominees on ethics, climate Lawmakers prep for coming wave of self-driving cars MORE (D-Mass.) said banks have plenty of money to send out solicitations for new products and that their arguments about the cost of these privacy policy notices should therefore be ignored.

"[I]f you ask them to just provide a scintilla of information on what privacy rights they have ... the banks say, 'Oh no, that's too expensive, we can't do that,' " he said.

Rep. Joe Barton (R-Texas) said he believes the annual notice should be kept to ensure banks don't take other steps at eroding the rights of their customers.

"When you start down that slippery slope that you know you don't have to notify privacy protection, the next step is to not even have privacy at all," Barton said.

Rep. Brad Sherman (D-Calif.), one of the supporters of the bill, rejected the idea that there is any value in mailing customers the same copy of a privacy policy each year. "The idea that you're mailed a copy of what you've already been mailed a copy of that hasn't changed, that does little or nothing to provide additional privacy, except we can say, 'Oh, we're for privacy,' " he said.

The bill is likely to be passed on Tuesday under a suspension of the rules, which requires a two-thirds majority vote. The bill might have been approved by voice vote, but Sherman asked for a roll call vote to create another roll call vote on Tuesday, which he called an "act of collegiality, showing that I think we ought to spend more time with each other."

Soon after debate ended, the House adjourned early in order for members to attend the White House Congressional Ball tonight.