Scenario 1: The Pope is accused of heresy. A group of Bishops, priests, and theologians — along with the usual collection of bloggers and video-making enthusiasts — issue a “formal correction” and they demand, in a filial way of course, that the Pope “repent”.
The Pope ignores them. Then they issue the second correction, as Saint Paul suggests. The Pope does not “repent”. So they publicly claim that he is deposed.
But the Pope continues to ignore them. He in fact remains on the See of Peter, and he continues to exercise papal authority. Deposition failed.
Scenario 2: The papal critics accuse the Pope of heresy. They issue a document which many persons sign. They loudly proclaim his guilty to the world. They establish a commission to examine the accusation, which confirms his teaching is heresy.
The Pope responds by defining his own teaching as dogma under Papal Infallibility, and by defining their position as heresy.
His teaching under Papal Infallibility cannot be wrong. They have no claim to infallibility. They are established as the ones who are heretics.
Scenario 3: Pope Francis restricts the Latin Mass, and makes rules requiring all priests to concelebrate and to say the Novus Ordo Mass every so often. This is a hypothetical, at this point in time.
The Latin Mass traditionalists break communion with the Pope and the body of Bishops, and they set out on their own, like the son who took his father’s inheritance and set out on his own.
They will end up with no Pope, no principle of unity. They will become divided into ever smaller groups. They will not agree among themselves on what is correct doctrine, and they have no Pope to settle their disagreements. Many of their followers fall away from the Faith altogether.
Summary
Popes cannot teach or commit heresy; they cannot fail in faith by apostasy or idolatry; they cannot err gravely in doctrine or discipline. All this is clearly established in my book. So if you are certain that the Pope has erred gravely, or is guilty of apostasy, heresy, or idolatry — you are certainly the one who is wrong.
RLCJ
the reproach of Christ 
Dear Friends,
An the Brief “Una cum tempore”?
Ad the cardinals Ottaviani and Bacci?
What do you think on this, please?
I don’t understand the question, sorry.
You have made the natural progression of disintegration very clear to me. It’s very scary because I can see this going on in a big way, now.
I am fighting my own demons and when I focus on the mess around me, which you draw attention to in your fine article, I feel totally drained and despondency creeps in.
John
The Faith and the Church are indefectible. No one can depose the Pope. They are hitting their heads against a brick wall. The teaching of the Church will continue to be filled with profound truths, and free from grave error, even in what is non-infallible. There is no need to worry. Faith in the true Magisterium. Ignore all shepherds who ignore or reject the Pope. Pray the Rosary and read Sacred Scripture. Believe what the Church teaches.
They already say he is a heretic. While he is not even too liberal (in their views liberal = heretic). The question is, will they go further from that verbal accusations, and how? Or will they await the next conclave hoping for a miracle to elect an ultra conservative. To me it looks like a sacrilege when they put on their blogs the Sacred Heart and the Immaculate Heart, the Holy Spirit and all the Saints, and turn all that towards the rest of us and towards the pope. As if God has divided Himself against Himself. A sin against the Holy Spirit, that is what they commit. May God be merciful to their souls, because I do not see how they can save their bodies when they have already denied those who could save them in time of cataclysm (as I explain in more detail in previous comments).