This one is pretty easy to refute. First, get an estimate of how many generations it should take for a species to go extinct because of genetic entropy. Then remember that mice go through three or four generations a year, and figure out how long ago mice would have gone extinct if the earth is 6,000 years old. I've heard 400 generations, which means mice should have gone extinct by at least 3,000 BC.
I'm not anti-Christian. I'm anti-stupid.