Is Trey Gowdy a member of the British House of Commons or a similar parliamentary system? If so, then he have a vote of “No Confidence" against the party leader. Otherwise, it doesn't work that way in the United States. You can't change leaders in the middle of a session.
In theory I suppose he call for a "no confidence" vote against Boehner and it could even pass, but it would have symbolic effect only (unlike in parliamentary systems where it would cause the government to immediately dissolve and new elections to be held).
Ironically, I most often see the "we're a Republic, not a democracy!" people demand "no confidence" votes, which just proves they don't know what a "Republic" is, and despite the fact they claim to defend it so much, they seem to prefer an old European style monarchy, complete with no confidence votes and government-appointed upper houses.
I hear you. as far as No Confidence goes. I don’t know what the correct terminology is, I only know that what we currently have as SOTH is a weepy pliable mound of jello that bends over backwards to go along-get along.
Until we get someone in that position that is willing to push back and actively fight this admin, this will continue.