AM radio towers are giant beasts thanks to the way AM radio works: amplitude modulation. The more power, the higher the band of the radio. This means that they are essentially radiating out broadcasts with lots and lots of energy, as opposed to FM radio. But just how dangerous are those towers? This Michigan State University Amateur Radio Club demo should give you a rough idea.
By attaching a jump cable to the tower, the amateur radio club at the university essentially shorts out the tower briefly. When that happens, the arc of electricity firing off the tower then carries enough strength to actually unleash the audio. There's about 50,000 watts in that tower and briefly in that arc. Hence, all the safety gear on the operator of this temporary unlicensed broadcast.
This is also, tangentially, why there's an FCC regulation known as Part 15. Essentially, Part 15 covers inadvertent radio interference that comes from electrical devices and poorly insulated coaxial cables. This loophole is often used to create legal, unlicensed radio stations on college campuses and other places, because the signal doesn't travel much farther than a small radius around the cable.
So, uhh, don't try this at home.