Hearings in front of the Republican-controlled House Financial Services Committee featuring Chopra have, for the last few years, focused on the many — many — complaints that GOP lawmakers have about the bureau and its leadership. While Wednesday's CFPB oversight hearing was no exception in lawmakers finding plenty to quibble with, committee Chairman Rep. Patrick McHenry gave a rare nod to a policy issue on which Chopra and his GOP critics have found common ground — data privacy for consumers in financial services. 

"To be clear, it's far from perfect, but I believe there is common ground between your proposal and the Data Privacy Act, which the committee advanced earlier this year," McHenry said. "We agree on the core of the issue — Americans should have greater control over their sensitive financial data. Consumers should know where their data is going, how it's used and be able to terminate collection of their data by certain firms."

McHenry said that he wants a law on the topic, not just a rulemaking that could be more easily overturned under a different director of the bureau. 

"To ensure our data privacy policy is not subject to the whims of any given administration, I believe it's critical that we make law — not just regulation. I hope we can work constructively on this issue moving forward so Americans' financial data privacy is protected for the long term," McHenry said. 

The CFPB proposal would give consumers a legal right to grant third parties access to bank account transaction data, while the GOP bill, though similar, aims to provide a consistent standard, lower confusion for consumers and give companies that hold consumer data a more straightforward set of rules to follow rather than a patchwork of state laws. 

To be sure, the majority of McHenry and other Republicans' comments aimed at Chopra were critical. McHenry said that the House would pursue a vote to nullify the CFPB's small-business data collection rule, as the Senate did in October. 

Republicans also questioned Chopra in his capacity as board member on the Federal Deposit Insurance Corp., which has come under scrutiny for its workplace culture. 

"As [a] CFPB director, you have a seat on the FDIC board, where you have made your presence known from the ousting of former FDIC Chairwoman McWilliams to the March bank failures," McHenry said. "In other words, you know what the heck is going on at the FDIC." 

In response to a question from Rep. Bill Huizenga, R-Mich., chairman of the panel's investigations subcommittee, Chopra reiterated that the FDIC board is investigating the allegations of sexual harassment of female examiners and a frat-house atmosphere.

"Certainly any type of these issues are serious, the board has created a bipartisan special committee that will have full authority to investigate it," Chopra said. 

The panel's ranking Democrat, Rep. Maxine Waters of California, pointed out that the Senate Banking Committee will hold a hearing featuring the CEOs of the largest banks next week, while the House will not. Waters said that she started regular hearings with big-bank CEOs during her term as chair of the panel and is disappointed that McHenry is not continuing to do so. 

"Our members deserve the same opportunity to conduct oversight of our nation's big banks," Waters said. "I hope the chairman will reconsider his decision and convene the CEOs for a hearing as soon as possible."