The far-right House Freedom Caucus has put House Minority Leader Kevin McCarthy (R-Calif.) in a tricky situation — they're calling to remove Nancy Pelosi (D-Calif.) from her post as House Speaker following her decision to bar two GOP picks from the Jan. 6 select committee, Politico reports.

In a letter sent Friday, the conservative group — which boasts incendiary members like Reps. Matt Gaetz (R-Fla.) and Paul Gosar (R-Ariz.) — asks McCarthy to "pursue the authorization of the House Republican Conference" and "bring up a privileged motion ... to vacate the chair and end Nancy Pelosi's authoritarian reign as speaker of the house." The caucus then contends that Pelosi's "tenure is destroying the House of Representatives" and its ability to "faithfully represent" the American people.

Pundits have pointed out that while the group's call to remove Pelosi has "no chance of succeeding," it does put McCarthy in a difficult position. If the minority leader were to initiate the motion, "it would further escalate partisan acrimony in the House," reports Politico. But if he doesn't, he runs the risk of losing House Freedom Caucus votes in his odyssey to become speaker. It's perhaps a sort of test.

Furthermore, should McCarthy move forward, he can certainly expect Democrats to "dish it back" down the line.

But again —  Democrats ultimately "have the votes to prevail" against any motion to implement such a measure. As Fox News' Chad Pergram points out, it's all a game of "multi-level chess."