Well a transformer is just that. Basically 10:1, or in this case 1:10, so that turns 12V in 120V. However, that is not outputting AC current, just 120V DC at low amperage. A string of LEDs or bulbs designed to run on 120V AC (Measured again in RMS, so that is 169+ to 169-, the RMS values we use is basically what you get when you measure the effective DC current of an AC sine wave.) wouldn't draw that much current, but in this situation batteries are used. For short durations you can draw a heck of a lot of power. That it isn't plugged in for very long is quite telling. Those little wires would probably not be able to sustain it.
AC systems can be run on DC if commutation isn't a factor. Get some quite nice effects with different types of bulbs. Most commercially available LED slight strips run at an effective 30Hz because of their diode nature. Running them at a 100% duty cycle on DC makes for a much more stable, and brighter, light output.