"When Cephas was come to Antioch, I withstood him to the face, because he was to be blamed." (Saint Paul, in his Epistle to the Galatians)
The powers of the Pope are not absolute -- quite the contrary: the most important and most recent dogmatic modern Ecumenical Council, Vatican I, makes clear that, "the Holy Spirit was promised to the successors of Peter not so that they might, by his revelation, make known some new doctrine, but that, by his assistance, they might religiously guard and faithfully expound the revelation or deposit of faith transmitted by the apostles." (Vatican I, Pastor Aeternus).
The 4 Cardinals who made their names public in the dubia (questions) on the apparent errors on Marriage and cohabitation present in the Apostolic Exhortation Amoris Laetitia are following stardard procedure. If the Pope (out of some personal sentiment) refuses to respond, he fails to live up to his obligation to confirm his brethren in the Faith handed down by the Apostles. This has consequences. The interview granted by Cardinal Burke (one of the signatories of the dubia, along with Cardinals Caffarra, Brandmuller, and Meisner) to the National Catholic Register makes clear what these consequences might be.
Some might argue that you are only four cardinals, among whom you’re the only one who is not retired, and this is not very representative of the entire Church. In that case, they might ask: Why should the Pope listen and respond to you?Well, numbers aren’t the issue. The issue is the truth. In the trial of St. Thomas More, someone told him that most of the English bishops had accepted the king’s order, but he said that may be true, but the saints in heaven did not accept it. That’s the point here. I would think that even though other cardinals did not sign this, they would share the same concern. But that doesn’t bother me. Even if we were one, two or three, if it’s a question of something that’s true and is essential to the salvation of souls, then it needs to be said.What happens if the Holy Father does not respond to your act of justice and charity and fails to give the clarification of the Church’s teaching that you hope to achieve?Then we would have to address that situation. There is, in the Tradition of the Church, the practice of correction of the Roman Pontiff. It is something that is clearly quite rare. But if there is no response to these questions, then I would say that it would be a question of taking a formal act of correction of a serious error.In a conflict between ecclesial authority and the Sacred Tradition of the Church, which one is binding on the believer and who has the authority to determine this?What’s binding is the Tradition. Ecclesial authority exists only in service of the Tradition. I think of that passage of St. Paul in the [Letter to the] Galatians (1:8), that if “even an angel should preach unto you any Gospel other than that which we preached unto you, let him be anathema.”
If the Pope were to teach grave error or heresy, which lawful authority can declare this and what would be the consequences?
It is the duty in such cases, and historically it has happened, of cardinals and bishops to make clear that the Pope is teaching error and to ask him to correct it.
This is an unprecedented moment in the post-medieval papacy, anyone who is sure of what will happen is not saying the truth. Perhaps nothing on the surface in the immediate future -- while strong currents violently destroy all that is not from God underneath. With the power of Teaching undermined, what is left of the papacy? The gardens and palaces of Vatican City, that Francis does not even like? Pope Bergoglio should tread carefully: these valiant Cardinals have nothing to lose.