Maybe, in other words, House Republicans need a speaker who’s an ambassador from the Tea Party to the G.O.P.’s K Street/Chamber of Commerce wing, rather than the other way around.

The reality is this: The only way the Republican House majority can become less dysfunctional and chaotic in the short run is if the next speaker wins the trust of enough conservative backbenchers to quell or crush revolts from the rest. And the best way to win that trust is to be seen as fundamentally on the insurgents’ side, which is a feat that Boehner, given his background and priorities, could never hope to manage.

Hence the recent appeal of drafting Paul Ryan to replace him. Ryan is the party’s leading policy entrepreneur, his blueprints have plainly pulled the G.O.P.’s center of gravity rightward, and he has stronger movement-conservative bona fides than anyone else in the House leadership.

The suspicions that the right always had about Boehner, and would have had about McCarthy — that they care more about the deal than about the outcome, more about the party’s donors than any defined small-government principle — does not attach to Ryan in the same way. So he would enter the job with a deposit of ideological credibility that might do more than all of Boehner’s backroom skills to keep (some) of the caucus’s rightward flank in line.

But Ryan is not really of the Tea Party. In the Bush era he voted for bills like No Child Left Behind, Medicare Part D, and TARP, all of which today’s conservative insurgents despise. And he’s a dove on immigration, the issue where the party’s base always expects — with good reason! — their leadership is poised to sell them out.