The following is a script of "Cardinal Seán" which aired on Nov. 16, 2014. Norah O'Donnell is the correspondent. L. Franklin Devine, producer.

At the heart of Pope Francis' revolution in the Catholic Church is a shy Franciscan friar, the pope's closest American advisor, Cardinal Seán O'Malley. The pope has appointed him president of the Church's crucial new commission to combat child abuse and named him a member of the Council of Cardinals, the pope's small "kitchen cabinet" charged with helping redraw the way the church is governed.

Soft-spoken and unassuming, he is usually dressed in the brown habit of his Capuchin Franciscan order and not in a Cardinal's red robes. He goes by "Cardinal Seán." And like Pope Francis, he is more inclined to conversation than condemnation. He commutes to Rome from his day job as archbishop of Boston to help Francis remake an ancient institution.

Cardinal Seán O'Malley: It's a very different world now because of his style.

Part of that style includes the pope's reliance on advisors like Cardinal Seán O'Malley. O'Malley not only works closely with the pope, but stays with him at the Vatican guesthouse when he comes to Rome on business.

Norah O'Donnell: When you come here to Rome, you stay at the Domus Sanctae Marthae, which is just right over there.

Cardinal Seán O'Malley: Yes, ordinarily. Yeah.

Norah O'Donnell: That means you're roommates with the pope.

"I think even here, particularly in the past, there was the feeling that this was an American problem."

Cardinal Seán O'Malley: Well, yes, you see him at all the meals. And very often will go and celebrate mass with him in the morning. And we have our meetings right there.

Cardinal O'Malley and then-Cardinal Jorge Bergoglio of Buenos Aires became fast friends when the Boston archbishop visited Argentina on church business in 2010. If you want to understand Pope Francis, you'd do well to look at Cardinal O'Malley.

Norah O'Donnell: You knew him before. I mean, did you know that he would be this kind of a leader?

Cardinal Seán O'Malley: I knew that he would be different. I am delighted that he is beyond my expectations.

Both share the same outlook -- open, non-judgmental, given to simple living, and not afraid to consider change.

One change is the pope's recognition that child abuse is a church-wide problem that can no longer be ignored or covered up by bishops. O'Malley has more experience than any bishop in the church when it comes to cleaning up child abuse. And Pope Francis turned to him to lead a new child protection commission for the entire church.

Cardinal Seán O'Malley: Well, it's something that I brought to the Commission of Cardinals and we've talked about it. And the cardinals were very, very supportive. And the Holy Father, he's a great listener

Norah O'Donnell: Has the Vatican resisted it in the past?

Cardinal Seán O'Malley: I think even here, particularly in the past, there was the feeling that this was an American problem.

Norah O'Donnell: But is there a recognition inside the Vatican that this is intolerable.

Cardinal Seán O'Malley: Certainly, the Holy Father is very, very aware of that and very committed to zero tolerance and to responding in a proper way to this phenomenon of child abuse.

Despite his office and influence in Rome, Cardinal O'Malley is a modest man, reluctant to put himself forward. He is humble, a true Franciscan, who would rather be addressed as "Cardinal Seán," than "your Eminence." It took more than a year to convince him to agree to an interview. But, he is so approachable you can talk with him about nearly anything.

Norah O'Donnell: Now, your shoes look a lot more comfortable than mine.

Cardinal Seán O'Malley: Well, 50 years of wearing sandals.

Norah O'Donnell: Well, do you ever have to wear closed-toe shoes?

Cardinal Seán O'Malley: Well, when I'm disguised as a cardinal.

Norah O'Donnell: Yes.

Cardinal Seán O'Malley: Which isn't very often.

His reputation for cleaning up the church began when he was installed as bishop of Fall River, Massachusetts, where O'Malley inherited one of the most notorious child abuse cases in history. Instead of lawyering up, O'Malley began reaching out directly to victims, settling cases and acting as a pastor, not a CEO. His success led to a transfer to Palm Beach, where the previous two bishops resigned after accusations of abuse. Then, in 2002, the Vatican sent him to Boston.

Norah O'Donnell: Were you worried?

Cardinal Seán O'Malley: Yes. Terrified.

Terrified because the Archdiocese of Boston, the onetime symbol of American Catholicism was dissolving, thanks to what was then the biggest sex abuse scandal in church history.

Cardinal Seán O'Malley: There were a thousand lawsuits against us. The seminary was empty. As I say such anger, disappointment, upset on the part of the people.

Norah O'Donnell: This was a pretty tough assignment?

Cardinal Seán O'Malley: It was -- somebody described it as a fixer-upper.

"Well, the pope and I aren't about texting."

And he began fixing it up on his first day on the job 11 years ago by doing something bishops seldom do: admitting what had happened and apologizing for it.

[Cardinal Seán O'Malley: At the beginning of this installation ceremony, I again ask forgiveness for all the harm done to young people by clergy, religious and hierarchy.]

Seán O'Malley set a new tone in Boston. The first thing he did was sell the palatial archbishop's residence and the 28 sprawling acres it sat on.

Cardinal Seán O'Malley: Well the archbishop's residence was more house than I needed.

Norah O'Donnell: Did you realize how big an impact it would have, that decision?

Cardinal Seán O'Malley: Well, I knew it would have an economic impact on the diocese. And at the time I was very grateful that we had this mansion to unload and because we sold it for over 100 million dollars.

O'Malley moved into the modest cathedral rectory. He has a deep devotion to working with the poor, particularly immigrants. And is a prominent voice -- in any of eight languages -- in the Catholic Church's call for immigration reform. Earlier this year he led a mass at the border wall in Nogales, Arizona, even distributing communion through the fence to call attention to the problem and the church's position on reform. The pope, who has been a strong voice for immigrant rights, called it "a powerful picture."

But it's O'Malley's work to reform the church on child abuse where he has made the biggest impact.

Norah O'Donnell: For many people outside the church and inside the church, the biggest scandal isn't the predators, it's the bishops. The bishops who protected them and lied about them and moved them from parish to parish. And many of these predators have been prosecuted. But the bishops have not. Why is that?

Cardinal Seán O'Malley: One of the first things that came up is the importance of accountability. And we're looking at how the church could have protocols, how to respond when a bishop has not been responsible for the protection of children in his diocese.

Norah O'Donnell: I want to ask you about Robert Finn, who is the bishop of Kansas City/St. Joseph and, as you know, he pleaded guilty to a criminal misdemeanor for not reporting one of his priests to authorities. Bishop Finn wouldn't be able to teach Sunday school in Boston.

Cardinal Seán O'Malley: That's right.

Norah O'Donnell: How is that zero tolerance...

Cardinal Seán O'Malley: Well...

Norah O'Donnell: ...that he's still in place? What does it say to Catholics?

Cardinal Seán O'Malley: Well, it's a question that the Holy See needs to address urgently.

Norah O'Donnell: And there's a recognition?

Cardinal Seán O'Malley: There's a recognition of that.

Norah O'Donnell: From Pope Francis?

Cardinal Seán O'Malley: From Pope Francis.

The cardinal's careful candor isn't limited to the church's mishandling of abuse. Take the Vatican doctrine office's crackdown on American nuns for focusing more on social justice than issues like abortion and contraception -- placing the nuns under the supervision of three bishops.

Norah O'Donnell: It looked like a crackdown from men at the Vatican on...

Cardinal Seán O'Malley: A disaster.

Norah O'Donnell: A disaster?

Cardinal Seán O'Malley: Disaster.

Norah O'Donnell: Should there be more women in positions of power in the Curia?

Cardinal Seán O'Malley: Yes. I think there should be. And hopefully, there will be.

Norah O'Donnell: When?

Cardinal Seán O'Malley: Well, I can't tell you what time, but hopefully soon, you know.

"...If I were founding a church, you know, I'd love to have women priests."

So far, there is little in the way of concrete change, but Cardinal O'Malley spends about one week every other month in Rome, otherwise he and the pope stay in contact using a technology that seems almost as dated as illuminated manuscripts.

Cardinal Seán O'Malley: Usually the, we fax.

Norah O'Donnell: Really?

Cardinal Seán O'Malley: Yes.

Norah O'Donnell: You fax with the pope?

Cardinal Seán O'Malley: Yes.

Norah O'Donnell: People still communicate by fax?

Cardinal Seán O'Malley: Still communicate by fax.

Norah O'Donnell: Like, with letters or...

Cardinal Seán O'Malley: Uh-huh.

Norah O'Donnell: Really?

Cardinal Seán O'Malley: Oh. Very quick and efficient. And a little more private than...

Norah O'Donnell: Most people think...

Cardinal Seán O'Malley: Safer.

Norah O'Donnell: Oh, really?

Cardinal Seán O'Malley: Uh-huh.

Norah O'Donnell: Most people think texting is quicker than faxing.

Cardinal Seán O'Malley: Well, the pope and I aren't about texting.

His choice of communication technology is not the only thing conservative about him. Church traditionalists accuse him of being a closet liberal for participating in ecumenical services and presiding at the funeral of abortion rights supporter Ted Kennedy. But the cardinal is a hard-liner on Catholic doctrine. Like Pope Francis, he upholds traditional positions on abortion, gay marriage, birth control and women's ordination.

Norah O'Donnell: The church says it's not open to the discussion about ordaining women. Why not?

Cardinal Seán O'Malley: Not everyone needs to be ordained to have an important role in the life of the church. Women run the Catholic charities, the Catholic schools, the development office for the archdiocese.

Norah O'Donnell: Some would say women do a lot of the work but have very little power.

Cardinal Seán O'Malley: Well "power" is not a word that we like to use in the church. It's more service.

Norah O'Donnell: But they can't preach. They can't administer the sacraments.

Cardinal Seán O'Malley: Well...

Norah O'Donnell: I mean, some women feel like they're second class Catholics because they can't do those things that are very important.

Cardinal Seán O'Malley: Well, they, but they're, they have other very important roles that, you know, a priest cannot be a mother, either. The tradition of the church is that we have always ordained men. And that the priesthood reflects the incarnation of Christ, who in his humanity is a man.

Norah O'Donnell: But in spite of that, does the exclusion of women seem at all immoral?

Cardinal Seán O'Malley: Well, Christ would never ask us to do something immoral. And I know that women in...

Norah O'Donnell: The sense of equality. I mean, just the sense of sort of the fairness of it, you know. You wouldn't exclude someone based on race. But yet you do exclude people based on gender.

Cardinal Seán O'Malley: Well, it's a matter of vocation. And what God has given to us. And this is, you know, if I were founding a church, you know, I'd love to have women priests. But Christ founded it and what he he has given us is something different.

But God is not afraid of change, as Pope Francis has told his bishops. And Cardinal O'Malley is thrilled with his old friend.

Cardinal Seán O'Malley: I always had admiration for him but to see how he has made this extraordinary impact on the church is so gratifying.

Norah O'Donnell: And will change the future of this church.

Cardinal Seán O'Malley: There's no doubt.