Engine turns over but sometimes won't start?

It could be a bad fuel pump. But because it only has trouble starting in the morning, it is most likely a small animal (such as a kitten or a squirrel), that climbed into the engine bay in search of warmth and shelter during the night. When you attempt to start the vehicle, the tail of the animal is often somewhere near the crank case, because the part of the engine that holds heat the longest is the oil pan (directly below the crank case) and the animal can be sucked into the crankshaft and mangled like fruit in a blender. Their friends can often times smell their blood, and climb into the engine bay to rescue him, and the cycle repeats itself. You seriously might want to check your oil pan for blood.