If it is a larger tap, like a 12mm for a head stud and it is flush with the block or there is alot of it in the hole, I don't think I would try breaking it up with a hammer and punch. The weld method works on bolts real well. The tap extractor will work best if the tap broke because it was subjected to side pressure. If it broke due to chip build up or too much pressure when it bottomed out, it will be tight. You might want to take short piece of steel rod and stick it on top of the tap and strike it with a hammer a couple of times. If you use a piece of material that is softer than the tap, it tends to not break the tap. that will sometimes relieve the pressure on the side of the thread that is driving the tap downward. Then try the tap extractor. If it is not too deep in the hole some times you can cut an "x" shape on the end of a piece of steel with a thin fiber wheel and drive it down on top of the tap with the tabs of the X going down into the chip relief areas cut into the tap.