(CNN) A growing group of rank-and-file House Republicans wants House Minority Leader Kevin McCarthy and GOP leadership to punish Reps. Liz Cheney and Adam Kinzinger for accepting a position from House Speaker Nancy Pelosi to serve on the select committee investigating the January 6 insurrection.
The push to seek punishment rose to a new level on Sunday, after Pelosi announced that Kinzinger had accepted her invitation to join the committee. Initially, most rank-and-file Republicans were content to let Cheney serve without much of a fight, but Kinzinger's addition has changed the conversation and has put a new level of pressure on McCarthy.
While the loudest cries have come from members of the hard-right Freedom Caucus, sources say that the sentiment has started to spread beyond the hard-line crew.
"There's a lot," said one GOP member about the push to have the pair removed from their other committees. "Supporting Pelosi's unprecedented move to reject McCarthy's picks was a bridge too far."
Pelosi rejected two of McCathy's choices last week -- Reps. Jim Banks of Indiana and Jim Jordan of Ohio -- which prompted the GOP leader to withdraw all five of his picks.
Rep. Scott Perry, a Freedom Caucus member, publicly called on Conference Chair Elise Stefanik to call a special GOP conference meeting to "address appropriate measures" related to Pelosi booting two of McCarthy's chosen picks from the committee. Some members specifically want McCarthy and Stefanik to push for a vote of GOP members to strip Cheney and Kinzinger, who both voted to impeach former President Donald Trump earlier this year, from their other committee assignments. Stefanik's office did not respond to a request for comment on Perry's desire for a conference meeting.
But kicking them off their committees would be easier said than done. While McCarthy could remove Cheney and Kinzinger from their other committees, the Democratic majority ultimately controls committee membership. Appointments to standing committees are privileged resolutions that come at the direction of the caucus. The GOP conference could direct the removal of Cheney and Kinzinger and the resolution would be offered on the floor. Those appointments, under normal circumstances, are generally adopted by unanimous consent. However in this unique situation, a recorded vote could be called and Democrats have the votes to defeat the removal resolution. While Pelosi herself has the power to appoint any member she chooses to select committees, under House rules one party cannot offer a privileged resolution appointing members of the opposite party to a committee.
The scuttle demonstrates how difficult McCarthy's leadership role remains. While conservatives applauded his decision to attempt to appoint both Banks and Jordan and his subsequent move to pull back all of his choices, they still believe Cheney and Kinzinger need to be reprimanded for not remaining loyal to the conference.
McCarthy's office did not respond to questions about Republicans pushing him to punish Kinzinger and Cheney.
Sources say McCarthy and GOP leadership have no appetite to get involved in a protracted battle over punishing Cheney and Kinzinger. But when Pelosi first suggested she might appoint a Republican to the committee, McCarthy warned a group of freshman Republican that if one of them were to accept an appointment from the speaker, they should plan on getting all their committee assignments from her. Now members are pointing to McCarthy's threat and clamoring for action.
"Plenty of people wondering the same things," another GOP member said. "If they are accepting appointments from Nancy Pelosi rather than the GOP, haven't they already effectively left? Perhaps they should ask Speaker Pelosi for committee assignments?"
The Freedom Caucus is already pressing McCarthy to file a motion to vacate Pelosi from the speakership. McCarthy has not weighed in on their push, which has no chance of passing. But a Freedom Caucus source told CNN that if McCarthy does not become actively involved in the motion to vacate, that could amplify calls for him to remove Cheney and Kinzinger from their committees, with the group eager to seek payback in some way.
A spokesperson for Kinzinger suggested if McCarthy chose to punish the duo it would be an example of a bigger problem with his leadership.
"It would speak volumes if he took away their committee assignments for upholding their oath to protecting our democracy," said Maura Gillespie, Kinzinger's communications director.
Cheney has already signaled that she was not worried about being kicked off committees as punishment for serving on the select committee.
"My oath, my duty, all of our oaths, all of our duty are to the Constitution and that will always be my focus, not politics," she said after Pelosi first announced her appointment earlier this month.