Can you become so evil that you strike the "delete" button and erase the natural law from your heart? In order to answer this question, we must first define "natural law."
Natural law relates to the inclination in human nature that inclines us to the good. Saint Thomas defines the first precept of natural law as" "good is to be done and pursued, and evil is to be avoided."
It would seem that natural law could in fact be erased from the human heart since we can lose the Holy Spirit and sanctifying grace - both of which are greater than natural law. However, this is not the case because the Holy Spirit and sanctifying grace are granted to human nature - they are not natural to man. Natural law, on the other hand, is just that: natural. So long as a person has "human nature" his nature is oriented naturally to the good. We all still have human nature and so we all still have natural law - no matter how evil you are.
Now then, the tragedy of original sin has introduced into us concupiscence. Concupiscence is the "law of sin" that Saint Paul speak of in Romans 6-7. Our passions (e.g. desire, hate, etc.) are no longer rightfully submitted to our intellect and will. And so we often follow our passions in an unreasonable way. For example, our disordered passions lead us to eat too much pizza, drink too much alcohol, hate our neighbor, lust, etc.
By the way, Saint Thomas Aquinas identifies 11 passions in human nature. The passions are not evil. They just need to be guided by reason:
1. love (amor)In Adam and Eve before the fall, and in Jesus and Mary, the human passions were perfectly submitted to the intellect and will. It looked like this: Intellect > Will > Passions. After the fall of our first parents, our passions have been trying to run the show. Saint Paul refers to the passions collectively as "the flesh."
2. hatred (odium)
3. desire (desiderium)
4. aversion (aversio or fuga)
5. joy (delectatio, gaudium, or laetitia)
6. sorrow (tristitia)
7. hope (spes)
8. courage (audacia)
9. despair (desperatio)
10. fear (timor)
11. anger (ira)
No then, Saint Thomas holds that our inordinate passions do not destroy our human nature. We are not strictly "totally depraved." We are disordered. Since human nature is preserved, so also, natural law will always be preserved. This, by the way, is the explicit teaching Saint Augustine:
"Thy law is written in the hearts of men, which iniquity itself effaces not." -Augustine Confessions 2.Oh if Protestants would return to this Augustinian teaching. It's at the center of the Catholic doctrine of salvation. There is something still good in man, but this is not a moral goodness (we are conceived with original sin). Rather, it is a natural inclination to the good. The problem is that our passions lead us to think that beer, sex, fame, money, or whatever is "the good" and there is where we get into trouble.
The gift of sanctifying grace given at justification allows for the human person to be transformed and renewed. In short, it allows the intellect to pick up the reigns and start whipping those passions into the shape.
Thomas grants that the secondary precepts of natural law can be erased from the human heart (i.e. sodomy is sinful), but the general or abstract principle (pursue and do the good) cannot be erased. See Summa theologiae I-II q. 94, a. 2 resp.