I've been hearing this aalll day long!
"all our friends get to open one on Christmas Eve", " Everybody I know opens one gift on Christmas Eve", "some of my friends open all their gifts on Christmas Eve", etc, etc....
I told them that for each time they ask for the rest of the day(this was at about 3pm) that I would take one present from under the tree and save it for their birthday. They haven't asked since.