All normal mini incandescent & LED strings have a pair of 3a fuses in the plug, When connecting sets together I've found you have to keep it below 2a or you'll pop the fuse.
Short from midpoint in the string (in series with some LEDs and the ballasting device), a short to rusty metal surface (high resistance there) or to metal parts that have weak connection to Earth won't pull much current. May well stay below 3A
3A at 120V is a lot of power. If this power dissipates in a bad place - like a screw going through the electrified gutter and lightly touching something else inside the wall which is Earthed, is able to dissipate several 10's Watts in localised heat. Thats about as much power as flame from a lighter
