When Pope Benedict XVI announced in February that he would be stepping down, it was suggested that Cardinal Timothy Dolan, the conservative archbishop of New York, might replace him, making Mr. Dolan the first American to ascend to the papacy. The cardinal has laughed off the idea, but the fact that the question was even raised suggests how influential a figure Mr. Dolan—who has been referred to as “America’s pope”—really is. Since 2010, he has been the president of the United States Conference of Catholic Bishops, and despite the fact that the importance of religious leaders in public life has been waning in recent decades, Mr. Dolan, a Roman Catholic, manages to stand out in the national conversation. Last year, he led the charge against President Obama’s contraception plan, which required that religious institutions provide employees with insurance for contraception, among other things. Mr. Dolan considered the plan an affront to the morals and values of the Church, and, if you’ll recall, the issue spurred a raw, volatile, heated public debate that involved Rush Limbaugh, who called Georgetown University law student Sandra Fluke a “slut” and a “prostitute” for supporting the plan. Mr. Dolan did not sink to using such invective, though he doesn’t have a completely uncontroversial track record. When Mr. Dolan was the archbishop of Milwaukee, it has been revealed, he signed off on providing as much as $20,000 to sexually abusive priests in exchange for their agreeing to be defrocked. Although Mr. Dolan is a staunchly conservative figure, he has shown signs of open-mindedness. Last year, he got behind the canonization of Dorothy Day, the Christian anarchist, and, in September, in a sign of great equanimity, he gave the closing benediction at the Democratic National Convention.