Yikes! You drop one little paragraph break, and all heck breaks loose. Sorry about that!:-)
There is no faction in the SSPX that favors schism, if you mean a formal breaking of ties with the Church. Certainly, there is some "tension" involved in respecting the office of the Pope while believing that he has taken positions that are contrary to Catholic teachings. The SSPX does a pretty good job of addressing the positions without disrespecting their source, IMO.
No schismatic believes he is ever breaking ties with the Church. He always believes that the Church is breaking ties with him.
My point was that there is a faction that simply does not care if the SSPX ever fully reconciles with the Holy See.