New York’s Cardinal Timothy Dolan is the most media-savvy of the current crop of senior American prelates by a country mile, and it’s a good thing, because today he faces a classic “damned if you do, damned if you don’t” PR trap.

Stereotypically, Dolan is seen as a vintage “John Paul II” bishop, uncompromising about Catholic orthodoxy. When he was elected president of the US bishops in 2010, it was seen as ratifying a conservative ascendancy in the American hierarchy, and when Time magazine named him one of the 100 most influential people in the world in 2012, it was due partly to his reputation as an intimate of John Paul’s right-hand man, Pope Benedict XVI.

In the Francis era, however, a new wind is blowing in Catholicism, less about the culture wars and more about the social gospel, which can put prelates like Dolan in a tight spot.

When he sticks to his guns, such as defending the US bishops’ battles with the Obama administration over contraception, he’s accused of not getting on board. When he does something associated with Francis’ agenda, such as speaking out for immigrant rights, cynics grouse he’s sucking up to the new boss.

What’s an image-conscious cardinal to do? As a New Yorker might say, Dolan’s answer boils down to “fuggedaboutit” and embrace the big picture, which is that Francis has given the Catholic Church an almost miraculous public “facelift.”

“This is a Church that used to have a face of being old, craggy, and nay-saying,” Dolan said. “Now it’s thought of as young, exciting, daring.”

From his perch on Madison Avenue, the marketing and PR center of the universe, Dolan said he’d like to “send a dozen roses” to Francis for making his job easier. So strong is his satisfaction, in fact, that Dolan’s lone real complaint at this stage is the difficulty of getting Coach Tom Coughlin of the New York Giants, a Catholic, into the pope’s morning Mass.

Dolan knows a winning personality when he sees one, since he’s no slouch himself in the charm department. He has the gift of gab of an AM radio talk show host, a job his brother Bob actually had with WISN in Milwaukee, and the sense of humor of a late-night comedian.

Example: Dolan is a St. Louis native, and when named to New York he was asked what he’d do if the Cardinals and Yankees ever square off in the World Series. Under those circumstances, he shot back, “I’d become the first pro-choice Archbishop of New York!”

Read John Allen’s exclusive interview with Cardinal Dolan