I agree with bcat above. The worst thing that can happen is that they won't give you a deferral and you'll have to decide whether to attend, or withdraw. But you won't get rejected just for asking.
As for what's required to gain a deferral, I would think that would really vary school by school and person by person. Also, if the school is over-enrolled (i.e., they misjudged and more people decided to hold onto acceptances than they intended), they just may grant you a deferral quite easily. So, you may as well give it a shot. But I would definitely try to make the strongest case possible. You could also do some searches on SDN to find stories of successful deferral requests. I've certainly heard of it in the context of a sick family member that needed to be cared for, or a pregnancy. But I'm sure there are other instances as well (perhaps an amazing once-in-a-lifetime opportunity that would really complement an MD?).