Lee: Obama 'trampling' on Constitution with recess appointments

Support and outrage of the move has largely broken down along partisan lines, but Lee argued that his staunch opposition to the move was not based in party politics.

"America is not a government of one. These are real rights that the president has trampled," he said Wednesday. "I would be just as hard on any Republican president that tried this nonsense."

Lee's comments came as he testified before the House Oversight Committee, which was holding a hearing on the appointments. The Utah Republican was invited to testify after he announced last week that in response to the president's action, he would challenge every upcoming nominee until those picks were rescinded.

GOP lawmakers have been searching for ways to fight back against the White House following those appointments. Some members have refused to acknowledge Cordray as a legitimate director, and Sen. Rand PaulRandal (Rand) Howard PaulHouse bill set to reignite debate on warrantless surveillance Authorizing military force is necessary, but insufficient GOP feuds with outside group over analysis of tax framework MORE (R-Ky.) plans to file an amicus brief supporting legal moves by several right-to-work groups challenging the NLRB appointments.

While it is widely expected the appointments will be challenged in court, Lee indicated in his comments that he did not think a member of the Senate could be the one filing suit.

"The most likely type of party that could establish standing would be a party aggrieved by an order [by one of those agencies]," he said.