A small Texas bank, together with two conservative advocacy groups, have filed suit against the Consumer Financial Protection Bureau, claiming that its powers and Obama's recess appointment of its director are unconstitutional.

The State National Bank of Big Spring, Tex., the Competitive Enterprise Institute and the 60 Plus Association, a conservative advocacy group for seniors, claim that Dodd-Frank effectively gives "unbounded power to the CFPB," resulting in "unprecedented violations of 'the basic concept of separation of powers' " laid out in the Constitution.

richard cordray, cfpb Richard Cordray (Bloomberg)

The lawsuit also alleges that President Obama's recess appointment of CFPB Director Richard Cordray was unconstitutional because it did not happen during an official Senate recess. Finally, it claims that the new Financial Stability Oversight Council is also unconstitutional for having "sweeping power and effectively unbridled discretion" to determine which banks are "too big to fail" and thus subject to greater oversight.

Republicans brought up many of these concerns about the CFPB from the start and have since proposed legislation to subject the CFPB to the congressional appropriations process and replace its single, presidentially appointed director with a five-person commission. The White House, however, has dismissed the complaints about Cordray's appointment, and Democrats have defended the CFPB's authority. In January, Senate Banking Committee Chair Tim Johnson listed the accountability measures for the new bureau, from audits by the comptroller general to the judicial review under the Administrative Procedures Act.

"This lawsuit appears to dredge up old arguments that have already been discredited," says Jen Howard, CFPB spokesperson. "We’re going to keep our focus on the important work Congress created us to do—making markets work for consumers and responsible providers."

But this is likely to be the first of only many challenges to the agency's authority: Shortly after Cordray's appointment, the U.S. Chamber of Commerce also suggested that it would consider legal action to curtail the CFPB.