He often took stands that differed from U.S. presidents, recalls CBS News Senior White House Correspondent Bill Plante.
John Paul's reign spanned the terms of five presidents. Republican or Democrat, they all sought him out.
Sure, Plante reflects, it was about the politics of religion. But it was also about the man himself.
"I'm not poetic enough to describe what it's like to be in his presence," the current Oval Office occupant once said.
John Paul was the first pope to visit the White House, invited by Jimmy Carter in 1979.
"In times of great need, God does send someone," Ronald Reagan said of John Paul.
Reagan, who met with the pope four times, took the then-controversial step of establishing formal diplomatic relations with the Vatican.
Nancy Reagan believes the two men -- both wounded in assassination attempts in 1981 -- shared an emotional tie.
On "CNN Late Edition," Mrs. Reagan said, "They were very much alike. I mean, these were two men who were former actors. They both loved the outdoors, sports…and they both had wonderful senses of humor."
John Paul was at home with Republicans, such as the first President Bush -- who cheered his stands against communism and abortion -- and Democrats, who hailed his concern for the poor and the Third World, and his opposition to the death penalty.
also had four visits with John Paul.
"He obviously didn't agree with the American law on abortion," Mr. Clinton says, "but that didn't affect our dealings. He was big in what he believed, and he didn't demean other people or demonize them."
The pope spoke out forcefully against the U.S. war in Iraq, and reproached George W. Bush about it, both in, at the last of their four visits.
But at that same meeting, Mr. Bush gave John Paul the Presidential Medal of Freedom.
American presidents may have been courting the Catholic vote when they visited the pope, Plante concludes, but John Paul -- often called "God's politician" -- was using those meetings for his agenda as well.