Dappled Things has a good discussion going about TSM ("Traditional Sexual Morality"):
My correspondent hits on another problem with a lack of natural-law principles in our ethical debate. The Christian moral code begins to look like an arbitrary set of rules and taboos, more or less unrelated to each other, with no support beyond this or that biblical text (for the evangelical) or this or that remembered injunction from the catechism or grandma (for the Catholic). "The rules don't make sense because they're not supposed to makes sense: this is just what good Catholics do (or don't do)." The problem with this is that the best we can hope for is that people will do the right thing simply because they're told to. The "why" gets lost, and we're left with positivism and arguments from authority.
Correct me if I'm wrong, but didn't Pope Paul VI's committee on birth control recommend to the pontiff that proscriptions against artificial birth control be lifted, partly on the basis that natural law was a weak argument (recall these were Catholic theologians)? While I'm no expert on natural law, I think intellectual arguments in the face of hormones are usually a poor match. E. Michael Jones' book Degenerate Moderns: Modernity As Rationalized Sexual Misbehavior nicely illustrates the hoops intellectuals will go through to justify sexual license. Certainly Garry Wills is unconvinced, and he presumably has an excellent grounding in natural law.
Personally, my re-conversion to traditional sexuality morality occurred in the context of seeking a closer relationship to God and realizing that I was out-of-step with my Christian (both Protestant and Catholic) concerning sexual morality. The final step, that of abandoning contraceptives, occurred only when I completely accepted the authority given to the Catholic Church.
Blind obedience is unsatisfactory, although some would say the merit received is higher ('blessed are those who don't see and still believe'). Surely during the Old Covenant there were laws which made no sense but which Jesus said must be obeyed (Matt.23:1-2 - "The scribes and the Pharisees sit on Moses' seat; so practice and observe whatever they tell you").
Ultimately I think the important thing is to show church teaching on sexual morality is not unreasonable, which is how natural law can help - not in proving to Protestants or anyone else that TSM is correct but just getting to the point that they can see it as a reasonable belief.