In a letter dated late last week, the Republican senators declared that Cordray's recess appointment and three others to the National Labor Relations Board "were unprecedented and unconstitutional."
"We intend jointly to file an amicus brief challenging the constitutionality of President Obama's appointments to the National Labor Relations Board and Consumer Financial Protection Bureau," the letter says.
The letter is signed by most Republicans in the Senate, including Banking Committee members Mike Crapo, Bob Corker, Jim DeMint, David Vitter, Mike Johanns, Pat Toomey, and Jerry Moran.
Sen. Richard Shelby, the top Republican on the panel and an outspoken opponent of the recess appointment, did not sign the letter but has not ruled out doing so.
A spokesman for the Alabama Republican said that the lawmaker will wait to see the details of the court case and the arguments involved before deciding whether to join.
To date, no one has challenged the Cordray selection in court, but the same is not true for the NLRB appointments. Lawyers for Flatbush Gardens apartment complex in Brooklyn have asked a judge to throw out a complaint from the NLRB, arguing the recess appointments are invalid.
Although the Senate was technically not in recess, President Obama made the appointments on Jan. 4, arguing the "pro-forma" sessions where no business was conducted were not valid. The Justice Department has issued a legal opinion supporting the decision, although it acknowledged it was likely to be challenged in court.
Senate Republicans are also asking Senate Majority Leader Harry Reid to clarify his position on the legality of "pro-forma" Senate sessions. Reid and Senate Democrats first used the tactic to prevent President George W. Bush from making recess appointments in his final two years in office.
"Despite the fact that you were indisputably the author of what became the routine use [of] pro forma sessions to prevent recess appointments…you have on multiple occasions publicly expressed your support for President Obama's efforts to bypass the Senate," says the letter, which was signed by 36 Senate Republicans. "It appears that you believe the importance of preserving [the] Senate's constitutional role in the nomination and appointment process varies depending on the political party of the President."