The right-wing commentary and President Trump's criticism of the FBI are part of a vicious circle. The TV hosts encourage Trump, then Trump supplies sound bites for their shows, and then the hosts are even more emboldened.

With Mueller's investigation of Russian interference in the 2016 election reaching closer to Trump's inner circle, Fox hosts like Sean Hannity continue to demand Mueller's firing. Every night, Hannity tells millions of viewers that Mueller's probe is a corrupt plot to take down Trump and reverse the outcome of the election. Trump is a big fan of Hannity's show, and the two men speak on a regular basis.

"The anti-Mueller rhetoric in conservative media right now is part of a feedback loop," Nicole Hemmer, the author of a book about conservative media, "Messengers of the Right," told CNNMoney.

"Conservative media personalities know Trump hates the investigation and wants it shut down," she said in an email. "They bash the investigation and Mueller, and when Trump sees that happening (say, on 'Fox & Friends') it reinforces his belief that the investigation is illegitimate and that he should do something to end it. The likely consequence is that this increases the odds of Trump attempting to fire Mueller."