It's a little bit frustrating that Budziszewski leads us on with his explanation of why the "new natural law" is vacuous, but then he stops short in order to maintain a position of objectivity (which is understandable).
And yet, this is the most important point of all. Classical Thomistic natural law is based on the REALITY OF CREATED NATURE. "New" natural law joins with modern philosophy in rejecting that fundamental basis. The school represented by George, Grisez and Finnis is considered "conservative" because they support natural law at all, and because they have been able (through the convoluted type of reasoning criticized by Budziszewski in the article) to reach some conservative conclusions. Yet in reality they are supporting the deconstruction of the realist epistemological approach that has been the only sane philosophy since Aristotle.
Hegel's dialectical method, as exemplified by Darwinism, is the only servicable foundation other than realism. This is where I believe there could be a fruitful union between Thomistic natural law and the school of intelligent design. Scholastic teleology fell out of favor because people stopped believing in creation. How could beings who evolved have been designed for a purpose? The "new" natural law philosophy will not accept classical thomism because they do not want to be grouped into the "flat earth society."
But "intelligent design" has demonstrated conclusively the fallacies of Darwinism and the reality of creation by an intelligent being. Therefore creation for a purpose as the classical foundation for natural law was always the correct and truly scientific basis for any realist philosophy.