By Melanie Zanona and Chandelis Duster, CNN
(CNN) -- Georgia Rep. Marjorie Taylor Greene, one of Donald Trump's staunchest allies in Congress, on Thursday laid out demands for a GOP leader to earn her vote for House Speaker if Republicans are able to retake the majority after the 2022 elections and cast doubt on House Minority Leader Kevin McCarthy being elected to the position.
"We know that Kevin McCarthy has a problem in our conference. He doesn't have the full support to be speaker," Greene said on an episode of Florida Rep. Matt Gaetz's podcast that aired Thursday morning. "He doesn't have the votes that are there, because there's many of us that are very unhappy about the failure to hold Republicans accountable, while conservatives like me, Paul Gosar, and many others just constantly take the abuse by the Democrats."
Greene, who previously told reporters she would be laying out a list of demands to earn her speaker vote, mentioned some of the challenges that lay ahead in McCarthy's quest for the speaker's gavel. Among her demands, the Republican told Gaetz she wants fellow GOP Reps. Adam Kinzinger of Illinois and Liz Cheney of Wyoming kicked out of the House Republican Conference for serving on the January 6 committee, something McCarthy has so far resisted. She also said she has no respect for current GOP leadership.
The command from Greene comes amid frustration from some Republicans with GOP House leadership as McCarthy eyes the House leadership position. Trump's allies in Congress -- who have voiced increasing skepticism and frustration with McCarthy in recent weeks -- have already started to flex their muscles in the potential race for speaker, which is still more than a year away.
Depending on the party's margins, McCarthy could have a math problem if these Trump allies stick together. The House Freedom Caucus, which denied McCarthy the speakership once before, is comprised of roughly 40 members.
Some in Trump's orbit, including Gaetz and Trump's former chief of staff Mark Meadows, have also teased that Trump should make a play for the speaker's gavel, a move that could be designed to put McCarthy on notice and remind him of the leverage that the MAGA wing of the party would have in a speaker's race.
Greene also wants to see moderate Rep. John Katko, a New York Republican and McCarthy ally, lose his top spot on the House Homeland Security Committee. Katko, who represents a key swing district, supported the bipartisan infrastructure law, voted to impeach Trump and supported the Democratic-led effort to remove Greene from her committees.
"Katko's not a Republican. He's a Democrat," Greene said. "Our conference and the NRCC needs to stop playing this majority-maker game."