Can the Magisterium Teach Heresy?

In a recent Open Letter to Si Si No No, Fr. Giovanni Cavalcoli, O.P. challenges the SSPX to take a clear and logically consistent position relative to the indefectibility of the Church and the infallibility of the Magisterium on matters of faith:

Is the Church’s Magisterium, in matters of faith, infallible or fallible? You have to choose.  It is here that we will see if you are truly Catholic or crypto-Protestants, or, despite your intentions to the contrary – crypto-Modernists. But at least the Modernists are coherent: as a principal, they have a relativist and evolutionist gnoseology. How can you, Thomists, who claim the existence of an immutable and definite truth and also see the Church as teacher of the truth, end up alongside the Protestants and Modernists by saying that the Church can err de facto in the doctrine of the truth?

The Magisterium is not only infallible when it proclaims or defines a dogma, but also when it simply teaches a truth of the faith or close to the faith, without declaring the need to define it. It is enough that is about matters of the faith, as in the case of the new conciliar doctrines. It is this teaching that is found in the [Motu Proprio] Ad tuendam fidem, which you most certainly know. Besides, when you negate infallibility, certainly with this you do not identify sic et simpliciter, the fallible with the actually false. And yet you do not exclude the possibility of error, you do not deny that in the future, that which is taught today will become false or show itself to be false.

Now this contrasts with the Divine mission of teaching the Gospel which was entrusted to the Church by Christ. Therefore, denying the infallibility of the Magisterium is against the faith and so it is heresy. The moment you accuse, even in a veiled way, the Council of having fallen into heresy, you do not realize that you have fallen in it yourselves.

THE CATECHISM OF ST. PIUS X
Q. Can the Church err in what she proposes for our belief?  
A. No, the Church cannot err in what she proposes for our belief, since according to the promise of Jesus Christ she is unfailingly assisted by the Holy Ghost.


UPDATE: The Response from Si Si No No

The response given by the editors of Si Si No No confirms the SSPX position that the Second Vatican Council represents a substantial rupture in faith.  According to the authors, the doctrine of the Magisterium can be multiple or different regarding even the "substance" of the faith:

The  Church as subject is always one; She is and will always be “pillar and sustainer of the Truth ”, even if the object or doctrine taught by Her may be multiple regarding “the way” and the “substance”. Now the Second Vatican Council is “pastoral”.... So the doctrine of Vatican II is different regarding “the way” of the other XX Councils preceding it and in some cases it even deviates from “the substance”.  

According to the authors, this deviation or rupture was made possible insofar as the Second Vatican Council did not intend to "define and bind belief" and, therefore, the criteria for an infallible divine assistance was not satisfied at the council.  Rather, the type of divine assistance operative at the Second Vatican Council was only of a fallible kind and therefore subject to err -- not only in practical-prudential or "pastoral" decisions -- but also with respect to the substance of the faith.