Pope Francis receives a constant stream of people at the Apostolic Palace, dignitaries from all backgrounds and faiths.

But President Biden's Friday visit to the Holy Father stands out from most others.  When two top Catholics get together and one of them supports a woman's right to abortion, there are obvious grounds for disagreement, at least behind the closed walls of the Vatican. But the devout Biden's inherently tricky position — he is personally pro-life though politically pro-choice — has ignited a fevered debate between U.S. bishops.

"You have the second most famous Catholic in the world after the pope going around saying that, you know, abortion should be legal," the Wall Street Journal's Vatican correspondent Frank Rocca tells Fox News, explaining the recent furore. "He's the second Catholic president in US history. So that makes it a big issue and not only with conservative Catholics, but with a number of bishops who have said that he they don't think that he should be receiving Communion."

Pope Francis delivers his Urbi et Orbi blessing after celebrating Easter Mass at St. Peter's Basilica at The Vatican Sunday, April 4, 2021, during the Covid-19 coronavirus pandemic. (Filippo Monteforte/Pool photo via AP) ((Filippo Monteforte/Pool photo via AP))

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For these U.S. bishops, House Speaker Nancy Pelosi's position is also problematic. These bishops are considering a public rebuke to Catholics who support policies which go against church doctrine.  A call to refuse them Communion.  That could happen as soon as next month.  It would be part of a carefully worded document but the message would be sharp.  The pope has pushed back at the brouhaha saying pastors should be pastors and leave politics aside.

He has added they should use "the style of God" to accompany the faithful with "closeness, compassion and tenderness."  The pope has said that as a pope, as bishop and as a priest, he has never excluded anyone from Communion.  But in an apparent attempt to drive a point to bishops that he has not waffled on abortion, Rocca pointed out, Pope Francis has stepped up his rhetoric on the subject in recent weeks.

"He's used very strong language. He's talked about it as murder. He says it's like hiring a hitman to solve a problem. So he wants to make it clear that he's not soft on abortion," Rocca said.

FILE - In this Wednesday, Jan. 20, 2021 file photo, President-elect Joe Biden and his wife, Jill Biden, attend Mass at the Cathedral of St. Matthew the Apostle during Inauguration Day ceremonies in Washington. When U.S. Catholic bishops hold their next national meeting in June 2021, they’ll be deciding whether to send a tougher-than-ever message to President Joe Biden and other Catholic politicians: Don’t partake of Communion if you persist in public advocacy of abortion rights. (AP Photo/Evan Vucci, File)

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Another reason the pope has taken the step of asking American bishops to back off their criticism may be that he is more pre-occupied with keeping peace on earth than policing doctrine.

"You've got a polarization in the United States," Gerry O'Connell, associate editor of America Media, said.  "That polarization has also seeped into the church. What the pope sees from here, what the Vatican has seen, and people have told me they've seen, is a threat to democracy around the world — the zones of freedom are being reduced. Democracy is being threatened, and the internet is being used also to undermine democracy."

The Catholic Church in theory has cause to celebrate that the U.S. finally has another Catholic president after a long interlude following John F. Kennedy. But while the pope's pet causes have been helping the poor and protecting the planet, the bishops have a different focus.

"They voted a couple years ago, to say that, that the struggle against abortion is the preeminent priority of the church in the United States," Rocca said. "And some of the more progressive bishops who identify themselves as allies of Pope Francis said this is not what the pope wants. This is wrong. It's a priority. But it's not the preeminent priority. It's not above fighting poverty or helping migrants or protecting the environment."

In fact, a recent Pew Research Center poll found more than half of Catholics believe abortion should be legal in most cases.

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On many issues, Biden and the pope are expected to be in lockstep.  It will be their fourth meeting. It will be private and the press will get some lines out of it.  But the real meat may be hidden from view.  And it may take time to stew.

Gerry O'Connell reminded us of how it sometimes goes with these meetings.  "If you think back to when President Obama came here in 2014, one of the things that didn't come out immediately was they had talked about how Cuba and the United States could overcome their divisions. We learned later that that that was a central part of that meeting. Who knows what will be the central part of the Biden-Francis meeting? Certainly the climate question. I think they're on the same page."

Issues around migration and vaccine access will no doubt also top the list.

Other items may remain a mystery, but for sure the bishops will be watching closely.