The pope said among other things that "the contemporary world ... demands that we confront every form of polarization" that divides it. As he spoke, Mr. Boehner, sitting behind him on the rostrum of the House chamber, characteristically fought back tears.
They may have been tears of joy from a former altar boy at his success in bringing the Holy Father to the U.S. Capitol. But the very next day, the speaker stunned the political world by announcing his resignation, thus confronting the polarization that has seized his own Republican caucus in the House.
Mr. Boehner, aware that the tea party Republicans and other ultraconservatives in his flock were gunning for his head anyway, decided to spare his loyal members the unpleasantness of going through an intraparty row, though enough Democrats probably would have voted to save his job.
But on CBS' "Face the Nation" Sunday, Mr. Boehner made clear that he had run out of patience with his no-compromise gang, set on opposing President Obama no matter what the issue. He openly ridiculed their pipedreams on what they could achieve, notably repeal of Obamacare, voted down multiple times.
Calling his would-be executioners "false prophets" who are "unrealistic about what can be done in government," Mr. Boehner sounded liberated from recent years of trying to placate them. He sang "Zip-a-dee doo-dah" as he approached one press conference microphone.
The speaker, departing the leadership and Congress as well at the end of next month, said he would try to get as much legislative work done as he could by then. "I don't want to leave my successor a dirty barn," he said. "So I want to clean up the barn a little bit before the next person gets here." The new speaker is expected to be House Majority Leader Kevin McCarthy.
Mr. Boehner's decision appears to avoid a threatened government shutdown by ultraconservatives demanding a cut-off of federal funding to Planned Parenthood. But will he want to invite a final round of slings and arrows from his Republican critics by yielding on raising the debt limit and other Obama demands before he goes out the door?
The disarray of the Grand Old Party is only compounded at this juncture by growing animosity among its 2016 presidential aspirants. One side finds the leading establishment figure, former Florida Gov. Jeb Bush, mired in the polls despite his wide money advantage. The other side offers the trio of non-politicians -- Donald Trump, Ben Carson and Carly Fiorina -- cashing in on the public anger toward the status quo.
Public opinion surveys since the second Republican debate suggest the Trump fever is beginning to break, as his brash and crass assaults on rival candidates grow ever more insulting and irrelevant to the high stakes involved.
At the same time, Dr. Carson's thoughtless or at least careless detour from being above the schoolyard muggings, with his own mugging of all Muslims as unsuitable for the nation's highest office, may well pop his bubble too. And Ms. Fiorina's defense of her business acumen is under greater scrutiny.
With the implosions of the campaigns of former Texas Gov. Rick Perry and Wisconsin Gov. Scott Walker, and the apparent abandonment of those insulting debate undercards for the hopeless longshots, the dust is beginning to settle.
The old Republican congressional leadership has been torn apart by the decline of moderation since the days of Everett Dirksen, Howard Baker and Bob Dole in the Senate, and of Charlie Halleck, Bob Michel and Gerry Ford in the House, as the party of Lincoln and even of Reagan seems to have lost its bearings.
Right now it appears to be a headless horseman devoid of direction and tradition as it gropes to find not only a responsible leader, But also a road map to national acceptance. The GOP enjoys near-record electoral success at the local, state and congressional levels. Yet it founders in its clumsy quest to claim governance of the whole nation.
Jules Witcover is a syndicated columnist and former long-time writer for The Baltimore Sun. His latest book is "The American Vice Presidency: From Irrelevance to Power" (Smithsonian Books). His email is email@example.com.