Is Trey Gowdy a member of the British House of Commons or a similar parliamentary system? If so, then he can 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 could 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.
anyone k w when Gowdy’s committee starts up?