In an interview with NBC's Kristen Welker, South Carolina Rep. Trey Gowdy (R) offered his honest — and correct — assessment of his party in Congress. Here's the key bit:

I think the House is bordering on ungovernable right now. ... Being speaker is a very difficult job. We need to have a family conversation and sometimes you have to hit rock bottom before that conversation starts. We're getting close.

Now, Gowdy was explaining to Welker why he wouldn't be interested in the soon-to-be vacant job as speaker of the House. But his reasoning is almost certainly why Paul Ryan isn't jumping at the job either, despite basically every establishment Republican in the country urging him to do it.

The problem for Ryan, Gowdy and anyone else who is thinking about being speaker can be explained in a very simple math problem. Republicans currently control 247 seats.  There are, roughly, 40 Republican members — the vast majority of whom identify with the tea party-affiliated Freedom Caucus — who will vote against the wishes of leadership on almost any major measure unless the leadership adopts a very conservative stance. If you subtract 40 from 247, you get 207 -- 11 votes short of what a speaker would need to pass a piece of legislation without relying on any Democratic votes.

A Republican speaker who needs to always lean on Democrats to pass anything doesn't really have all that much power. And every time he (or she) leans on Democrats to pass something, that power erodes even more. (See: Boehner, John.)

But, you say, if Ryan was speaker, the Freedom Caucus wouldn't rebel! They like Ryan! He is conservatives' favorite establishment guy!

And you'd be right (sort of). “Paul Ryan is a good man,” Ohio Rep. Jim Jordan, chair of the Freedom Caucus, said on “Fox News Sunday." “If he gets in the race, certainly our group would look favorably on him."

So yes, Ryan would — as we noted in this space last week — almost certainly be the only member of the GOP conference who could get the 218 votes needed to be speaker in a floor vote. But getting elected speaker — while a real accomplishment — is not the same thing as running the House effectively.

And that's where Ryan and the Freedom Caucus would almost certainly part ways. If past is prologue, what the tea party-aligned GOP members of the House want on any given piece of legislation is absolute adherence to conservative principles. So no raising of the debt ceiling. No budget if federal dollars for Planned Parenthood are included.

In fact, no compromise — with Senate Republicans, with the White House, with anyone — at all.  And that is where Ryan would run into trouble. At the core of being the leader of either the House or Senate is compromise — especially when the current occupant of the White House isn't in the same party that you are.

Ryan, Gowdy or anyone else who tried to "run" the House would, inevitably, be drawn into talks with Obama about how to cut a deal to keep the government open, or raise (or not) the debt ceiling. Being speaker is a powerful position, but you don't get the last and only word on how legislation turns out. There is a group in the House three dozen or so strong that chooses not to understand that dynamic or simply doesn't care.

That was the problem Boehner was confronted with again and again during his time as speaker. He would hold firm on the preferred conservative outcome and refuse to budge in negotiations with the White House. But as deadlines drew near — and things like shutting down the government over a dispute over funding Obamacare loomed — Boehner would always advocate for talking to Senate Democrats and the White House in hopes of cutting the most advantageous deal possible. But the tea party wing wanted no conversations, no deals. Boehner's hands were tied. The end.

It's hard to imagine the House under Ryan's control being all that much different. I think he might get some honeymoon period from the tea partiers, but they are simply not a go-along-to-get-along bunch by nature. And with some major fights coming up soon in Congress, it seems likely that the Freedom Caucus would revert back to their oppositional ways sooner rather than later.

The question for House Republicans — and again, Gowdy hit the nail on the head — is what "rock bottom" looks like. Rock bottom at the presidential level for the party came in 1964 when Barry Goldwater won the Republican nomination but proved too conservative for the country as a whole and won only 52 electoral votes against Lyndon Johnson.

Given how heavily gerrymandered most House districts are (along with the GOP's significant natural advantage on the House map, given the concentration of Democrats in urban areas), it's hard to imagine House Republicans suffering broad-scale electoral losses (or losing control of the majority) before the national redrawing of congressional lines in 2021. The one thing I can imagine that might meet the standards of "rock bottom" is if Ryan decides not to run for speaker and what follows is a protracted, nasty fight — the result of which is some sort of power-sharing deal within the GOP or, even more remarkably, with Democrats.

Those scenarios — especially a power-sharing deal with Democrats — seem very unlikely to me, which may mean that House Republicans are still a ways from rock bottom. But even if they haven't bottomed out just yet, that doesn't mean there is anyone in the party who can lead it in its current form. There isn't.