LED cct without resistors
An LED is not a quickblow fuse; it will not fail instantly if overdriven.

Failure isn't caused by current directly, it's caused by high junction temperature either destroying the junction or melting the bond wires. So if your current is limited to 60ma, that will heat up the LED slowly, probably at a rate where its leads will conduct away much of the heat. You will have shortened its life, and possibly distorted the colour, but it will most likely run for hours or days at this level of (limited) overcurrent.