I'm not super keen on a lot of natural law arguments. That's not to say that I think that they are wrong, or bad, but I'm just dubious of them. Why?
I am a historian. Historians like to make a distinction between a primary source and a secondary source - a primary source being a document that is and of itself a source of information, and a secondary source would be something that talks about other things. If I am doing research on George Washington - Washington's letters, official documents, etc. would be primary documents. A book by some other history writing about Washington would be secondary.
The primary sources are what they are. Secondary sources - they could be good, or they could be bad. They could be accurate, or they could be someone wanting to pound an agenda.
Natural Law arguments are a secondary sort of way of approaching theology. Does natural declare the wonders of the creation? Sure. Is the Law written on the hearts of man? Sure. Are there things that are (or at least should be) obviously bad to all? Yep.
But we are in possession of the Holy Scriptures, the Word of God, breathed by the Holy Spirit, the revelation of Christ Jesus, written so that we might believe and thus have life in Christ's Name. That's a pretty spectacular primary source.
So, when I see someone go on and on without relying upon it; if I see someone use Scripture to establish that there is Natural Law and then just go on and on about what they think Natural Law "obviously" implies... that makes me nervous, just as I'd get nervous if I read a history book that was lacking in primary sources and high on personal interpretation.
It's the same thing with Tradition. Tradition is a good thing... but it's not primary. If your arguments are based upon the tradition, well, that's nice, but it's not primary. It can only be a secondary, a supporting argument. Ditto Natural Law.
Natural Law arguments seem to be gaining in popularity, and I'm not sure why. Possibly it's a reaction against modern liberalism... I'd say even a condescension to liberalism (oh, you reject Scripture, um, well, here, let's try arguments on nature and reason to persuade you). Maybe its because people are wanting to influence society as a whole, and Scripture isn't the primary argument there - which I can understand. Natural Law is a great tool for the kingdom of the left.
But we are the Church - we are those who have the life giving Word of God. The love of the Law, especially the Law of man for order (i.e. tradition) or the love of Natural Law must never eclipse our first love.