Warren Quinn (Morality and Action, p. 125 et seq.) has argued, in favor of moral realism, that in experience and even in the natural sciences, a great deal of the information we are most certain about arises from primary perception, impossible to ground in reason (or anything but more primary perceptive turtles). If we are warranted in believing that there is a chair beneath our butt based on nothing more than primary perception, then we are equally warranted in having initial moral beliefs grounded on nothing but the feeling of wrongness.
We can do nothing but proceed from our primary perceptions, trusting them until given reason to doubt them. But we must realize that the obvious is merely a starting point. What is obvious to humans has not been demonstrated to reliably correlate with facts about the universe. Obviousness may inform the problem and even set priors, but it does not solve it.