Cardinal Burke is catching some heat from some bloggers I do respect, and who have been admirably defending Catholic teaching in the face of the worst parts of this document. I want to defend the Cardinal, mostly because I know him and am interpreting his statement in light of what I know of his character.
His Eminence has chosen to focus on the nature of an exhortation-- according to Cardinal Burke, quoting the pope, it is "not an act of the magisterium"; it is a "personal" document. Hence, nothing in it changes doctrine, and no pastoral practice that would change or defy doctrine can be divined from it.
That's it. No, he is not "taking on the pope" and every form of mischief the document (not to mention this papacy) has and will bring. You might be disappointed in that, but that is not his way. He is saying to the faithful remnant out there not, "See, there's nothing wrong!", but rather, "Though things are definitely bad please take heart that the Church is indefectible and that this truth is untouched, even by this."
We are being scourged. We need to be faithful. The Cardinal has it right, as far as he states. If you want more from him, I understand it, but at least consider that his strategy has its own value. He is no coward; I know this from experience. He loves the Church and is trying to make sense of this like we all are.