Is it "heavy" or "light"?
The older "heavy" (linear) supplies are basically nothing more than a transformer, bridge rectifier, and filter capacitor. It probably puts out 17V-18V at no current, sinking down to 12V at 1A or so. If you keep drawing current above 1A, the voltage will just keep sinking down below 12V until it catches on fire (I doubt there's any kind of fuse in there).
The newer "light" (switching) supplies will just keep a steady 12V over the 0A to 1A range. Beyond that...it depends who makes it. It could shut itself down in an orderly manner, its voltage could start to go down, it could catch on fire.
In any case, it's never a good idea to exceed the maximum current rating of a power supply.
The Quick Shield
: breakout all 28 pins to quick-connect terminals