At Cordray's first Senate hearing as CFPB head, GOP lawmakers said agency rules will face court challenges, causing uncertainty about which rules businesses need to follow, the Los Angeles Times reported.
"I can't imagine how anybody could maintain under the circumstances that your appointment and your service is valid," said Sen. Mike Johanns, R-Neb. "And I can't imagine then … how the actions you are taking will be upheld, and I think that's a very, very serious consequence for our nation."
Republicans had blocked confirmation votes on any nominee to head the agency, whose powers the GOP lawmakers want restricted, and had prevented the Senate from formally taking a recess for more than three days, in an effort to head off a recess appointment.
Republicans asserted Obama's appointment of Cordray was unconstitutional because it came when the Senate technically was still in session. But the president, with backing from the Justice Department, said the Senate's pro forma sessions were meant to stop him from making recess appointments.
Senate Republicans had blocked a vote on Cordray, a former Ohio attorney general, in December.
Sen. Bob Corker, R-Tenn., said there is "no question there's going to be constitutional challenges" to Cordray's appointment.
"I have been appointed as director," Cordray said. "There may be issues about that … but I now have legal obligations I'm supposed to carry out for this bureau. I'm going to do that."