Charles and David Koch. Sheldon Adelson. Karl Rove. George Soros. The index is long of those who aren’t running for president but will nevertheless influence the outcome. To the list we need to add Pope Francis. Unlike the others, the pontiff won’t be endorsing anyone, but given his coming visit to the United States and the strength of his message and popularity, he is poised to uniquely frame the debate.

Pope Francis’ ambitious travel schedule will take him to Latin America this summer and then Cuba (likely in early September) before he arrives in Washington on Sept. 22. There, he will meet with President Barack Obama and address a joint meeting of Congress, becoming the first pope to do so. Next, he heads to New York City for a visit to St. Patrick’s Cathedral and the National September 11 Memorial, and possibly will officiate Mass at Madison Square Garden. His North American trip concludes with a visit to Philadelphia on Sept. 26-27.

Get ready for wall-to-wall coverage, not only in the cities he visits, but around the world. And these events will unfold just as the summer has wound down and the presidential campaigns kick into high gear.

The pope will arrive soon after the GOP candidates have debated in Cleveland and at the Reagan Library in Simi Valley, Calif. While no date has been set, the Democratic candidates are expected to debate for the first time in late August.

Like the rest of us, those candidates will be attentive to what Pope Francis says while also being envious of his approval numbers. According to the Pew Research Center, among American Catholics, Pope Francis is almost as popular now as St. John Paul II, who in the middle (1990) of his papacy was favored by 93 percent of American Catholics. Pope Francis enjoys a 90 percent favorability rating among his flock and is viewed favorably by 70 percent of all Americans (up from 57 percent at his papal inauguration). Even a vast majority of the “nones” — no religious preference — like him (68 percent).

No wonder Hillary Clinton, a Methodist, tweeted at the pope in support of his call for equal pay for women: “Amen to this headline, @Pontifex! Hope to see more voices speaking out.” Among those who may be especially attentive to his holy word are the potential and declared presidential candidates who are Catholic, including Martin O’Malley, Jeb Bush, Marco Rubio, Rick Santorum, George Pataki, Chris Christie and Bobby Jindal.

While the pope remains steadfastly opposed to abortion and same-sex marriage — the Vatican called Ireland’s vote for gay marriage a “defeat for humanity” — the Vatican is expected to release an encyclical by July in which Pope Francis will address both climate change and the poor. Francis, a chemist before entering the seminary, has publicly endorsed the idea that human activity has contributed to climate change, and he has addressed capitalism’s need to “devour everything which stands in the way of increased profits.”

So the stage is set. The big question is what message he will deliver and whether the candidates will feel obliged to respond.

The recent beatification of Archbishop Oscar Romero is illustrative of the angst His Holiness could cause in some political circles. Romero, the Salvadoran archbishop executed during a Mass in 1980, is often associated with “liberation theology.” Those are fightin’ words to some on the right. Consider a Glenn Beck rant in 2010:

“(Barack Obama’s) individual salvation depends on collective salvation. What does that mean? Well, according to liberation theology, it means that salvation and redemption bought by Jesus comes in the form of political and social liberation for minorities from white oppression. Salvation is realized with minorities achieving economic and political parity via redistribution of wealth with whites.”

Michael Lee, an associate professor at Fordham University who has studied liberation theology, sees the pope as a potential “game changer” who is a “pendulum swing” from the papacy of St. John Paul II.

“You can no longer box the Catholic vote in a U.S. conservative box,” Lee said. “Here’s a pope who is going to release an encyclical on climate change and the poor ... who is staunchly opposed to abortion ... who has not ceded ground on same-sex union. So Francis is just kind of breaking up this right/left box that we have, but I think especially in his emphasis on social issues, like poverty, like climate change, there’s going to be some rethinking about what the Catholic vote is going to look like.”

Because of their nonmonolithic nature, Catholics will be an important constituency in 2016. One-quarter of 2012 voters were Catholic. According to the Pew Research Center, Obama received 54 percent of the Catholic vote in 2008, which fell to 50 percent in 2012. However, Hispanic Catholics still backed Obama in droves (72 percent in 2008 and 75 percent in 2012). Lee believes the pope’s greatest impact will be at the local level, with those who are charged with implementing his vision.

“I think his effect in visiting the United States is going to be giving different bishops freedom to speak a little bit more candidly,” Lee said. “You have a strong movement in the bishops’ conference on immigration, with positions that don’t quite square in the conservative mold. So I think you’re going to have Catholics on either end of the political spectrum finding justifications for their positions in different Catholic teaching, so it’s going to be a much more diverse kind of bloc in 2016.”

Opposed to abortion. Concerned about climate change. Against same-sex marriage. Advocate for the poor. Funny that a leader known for doctrine is not himself doctrinaire.

Michael Smerconish writes for The Philadelphia Inquirer and is the host of “Smerconish” on CNN.