II. The argument from Underlying Moral Consensus:
1. If morality were a subjective matter, we would expect to find sizable differences of fundamental principles amongst moral codes.
2. But there is, in general, agreement concerning fundamental principles amongst moral codes.
3. Therefore, morality is objective rather than subjective.
I think this is legitimately an argument against subjectivism, though it could also work as an argument against relativism. We often consider things to be objectively true when everyone agrees they are true. If I see a tree over there, and everyone agrees there is a tree over there, then we take it as objectively true that there is a tree over there. On the other hand, if I see a tree over there, and no one else does, then people will assume I am having a hallucination, a vision, or some such.
I don't think either premise is true, though. If morality is an evolved behavior, then we might expect there to be a fair amount of convergence among codes, without this implying that moral codes must be objective. On the other hand, moral codes exist or have existed in the past that allow infanticide, human sacrifice, huge inequalities in social standing, torture, slavery, and on and on, so I think it's hard to find common fundamental principles that all moral codes adhere to.
Morality-as-evolved-behavior seems to have the capacity to explain the observed range of moral codes better than morality-as-objective-truth.