In a large bowl, combine pulled pork, cream cheese and green chilis. Stir together until well combined. In a 9×13 casserole dish, place down a later of corn tortillas, then top with a third of the pulled pork mixture. Repeat the tortilla layer and pulled pork layer two times, ending with a layer of corn tortillas. Pour enchilada sauce over the casserole and cover the dish. Bake at 375 degrees for 40 minutes until bubbly. Carefully remove the cover and sprinkle cheese over the casserole. Place the casserole under the broiler for 3 minutes until the cheese is golden and bubbly.