But once that's done it will set up a potentially titanic fight later this year to keep the government open and raise the debt limit. And there will be a new House speaker who will have to take over the nearly impossible job of showing effective governance and satisfying conservatives constantly hungry for battles with President Barack Obama and congressional Democrats.
That speaker is likely to be House Majority Whip Kevin McCarthy who is next in line for the job and will have the support of most senior GOP leadership. But McCarthy, widely perceived as slightly to Boehner's left, is not entirely assured of a smooth path to the top job. Conservatives will likely want to push their own candidate who would be more inclined to push fights like the effort to defund Planned Parenthood in return for any measure to fund the government.
"He has a long record of distinguished service but it's time for new leadership," Rep. Tim Huelskamp, R-Kan., told Politico of Boehner's leadership. "Conservatives will be working together, it's not going to be one or two of us, we're going to make a deal."
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Conservatives will not likely be able to block McCarthy's ascension. But even if the California Republican glides into the speakership he will inherit the same dysfunction that made Boehner's job so difficult since he got the top post following the tea party wave election of 2010.
In fact, McCarthy's job may be even harder as presidential candidates from Donald Trump to Ted Cruz to Carly Fiorina pressure congressional Republicans to pursue constant confrontation with Obama and Democrats. There is little downside for presidential candidates in a GOP primary to push for big fights. They are not thinking about the impact any shutdown or debt limit fight might have on Republicans' general election prospects next year. They are instead desperately looking to appeal to hard core GOP primary voters who don't want to see any capitulation to Democrats.
Many House conservatives also occupy safe seats. The only threat they worry about is a challenge from a more conservative Republican in a primary. So when it comes time to fund the government and raise the debt limit later this year, they will be hungry to wring concessions from Democrats over spending levels, Planned Parenthood and potentially other issues.
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The White House in contrast will have no appetite for deal-making. And Hillary Clinton, under heavy pressure from the left and Sen. Bernie Sanders on the campaign trail, will be strongly inclined to pressure the party not to cave in to any demands from Republicans.
All of this will be happening this fall and winter as the Federal Reserve is likely to begin raising interest rates, setting up a challenging scenario for financial markets and American business. The uncertainty level over policy will only increase because in order to get the speakership, McCarthy is likely to have to make some promises to House conservatives that he will be tough in his approach to Democrats. And if he fails to live up to those promises in December, he could face the same kind of leadership challenges that Boehner had to deal with in his five years of speaker.
McCarthy on Friday said it was time to focus on "unifying" the Republican Party. But there is little reason to think he will actually be able to do it. Boehner, the ultimate institutionalist and loyal party man, could not do it even though he was beloved by many in the party.
Boehner, leaving after fulfilling a lifelong dream of having the pope speak to Congress, will bequeath to his successor a deeply divided party with twin goals of showing it can govern while also achieving conservative policy goals. Right now those goals cannot be achieved at the same time. And that could be very bad news markets that are already on edge and an economy that could easily falter if Washington once again descends into self-made chaos.
—Ben White is Politico's chief economic correspondent and a CNBC contributor. He also authors the daily tip sheet Politico Morning Money [politico.com/morningmoney]. Follow him on Twitter @morningmoneyben.