I think the good Cardinal Burke will have a good many Catholics behind him when the confrontation peaks; the real Catholics will be revealed.
I have also noticed that Cardinal Burke is now only referring to respecting the office of the Successor of Saint Peter; not Humble Jorge Bergoglio, himself.
In the same quote that you quoted, however, he mentions “correcting AL”. It does not sound like he will correct Bergolgio. Perhaps some will see that as hair splitting, but it doesn’t sound like he is going to come out and call Bergoglio a heretic.
Hence, I don’t think this formal act of correction is going to look anything like most are hoping it will look like.