For Republicans, the dilemma posed by Francis is compounded by the fact that many on their side have argued that religious faith should have a greater role in politics. In 2012, Republican presidential contender Rick Santorum made his own trip to Houston to argue that Kennedy had been wrong.

“On that day, Kennedy chose not just to dispel fear, he chose to expel faith,” Santorum said. “The idea of strict or absolute separation of church and state is not and never was the American model.”

But Santorum, who is running again in 2016, has said that some of what Francis says — for instance, that Catholics should not believe that their faith requires them to reproduce like rabbits — grates on him.

“It’s sometimes very difficult to listen to the pope and some of the things he says off the cuff, and this is one of them,” Santorum, a father of seven, told radio host Hugh Hewitt in January.