Blizzard have said that people will start to die in Nightmare playthrough.
Normal is pretty much the training wheels game, especially at the start where the mobs are not agressive and let you run past them without caring much plus they die easily. Once you get further into the Acts of Normal then things will get a bit tougher but the average gamer will play through without many issues just like you would if you played easy on most games.
In Nightmare there will be mobs with more abilities and they're more agressive, this is when people will start to be killed if they're wreckless or undergeared (rushing through Normal).