So why is he out? Basically because the obstructionism failed.

Republicans did manage to put a severe crimp on federal spending, which has grown much more slowly under Mr. Obama than it did under George W. Bush, or for that matter Ronald Reagan. The weakness of spending has, in turn, been a major headwind delaying recovery, probably the single biggest reason it has taken so long to bounce back from the 2007-2009 recession.

But the economy nonetheless did well enough for Mr. Obama to win re-election with a solid majority in 2012, and his victory ensured that his signature policy initiative, health-care reform — enacted before Republicans took control of the House — went into effect on schedule, despite the dozens of votes Mr. Boehner held calling for its repeal. Furthermore, Obamacare is working: the number of uninsured Americans has dropped sharply even as health-care costs seem to have come under control.

In other words, despite all Mr. Boehner’s efforts to bring him down, Mr. Obama is looking more and more like a highly successful president. For the base, which has never considered Mr. Obama legitimate — polling suggests that many Republicans believe that he wasn’t even born here — this is a nightmare. And all too many ambitious Republican politicians are willing to tell the base that it’s Mr. Boehner’s fault, that he just didn’t try blackmail hard enough.

This is nonsense, of course. In fact, the controversy over Planned Parenthood that probably triggered the Boehner exit — shut down the government in response to obviously doctored videos? — might have been custom-designed to illustrate just how crazy the G.O.P.’s extremists have become, how unrealistic they are about what confrontational politics can accomplish.

But Republican leaders who have encouraged the base to believe all kinds of untrue things are in no position to start preaching political rationality.

Mr. Boehner is quitting because he found himself caught between the limits of the politically possible and a base that lives in its own reality. But don’t cry for (or with) Mr. Boehner; cry for America, which must find a way to live with a G.O.P. gone mad.