• Marjorie Taylor Greene backed Kevin McCarthy's bid for House Speaker. 
• MyPillow CEO Mike Lindell said Greene broke her promise by doing so. 
• Lindell told the Daily Beast that the GOP should back Trump for speaker. 

MyPillow CEO Mike Lindell said GOP Rep-elect Marjorie Taylor Greene "broke her promise" by supporting US House Republican leader Kevin McCarthy for Speaker of the House. 

"I'm very surprised that the one — I won't name her name but it's Marjorie Taylor Greene — broke her promise," Lindell said on the far-right Be Reasonable podcast on Thursday. 

Both are staunch supporters of former President Donald Trump. Lindell also told The Daily Beast that House Republicans should back former Trump for Speaker of the House, a position that does not require the occupant to be a sitting member of Congress. 

"It's disappointing anyone that went for McCarthy because we need a different input to get a different output," Lindell told The Daily Beast. "And that includes Marjorie Taylor Greene."

Lawmakers in the US House of Representatives went through a historic 15 rounds of voting to elect McCarthy to the House speaker position.

Greene has recently lashed out against other prominent GOP members in the hard-right Republican Freedom Caucus for not supporting McCarthy.

Insider previously reported that Greene, who was stripped of her committee assignments last year, worked out a deal with McCarthy to be placed back on prominent committees if he wins.