A GFCI does NOT disconnect the power if there is too much current draw, it is NOT a circuit breaker and won't work like one. GFCI's are required within certain proximity of any water source, such as in the bathroom, or kitchen (or in the case of the picture in this thread, next to a sink). A GFCI outlet compares the current flowing INTO the outlet on the HOT side to the current flowing OUT of the outlet on the NEUTRAL side. If there is a difference (about 5 milliamps) then the outlet turns off. This is to protect you from shock.
However, in the case of a short, or other HIGH current draw, the current flow will be the same on both sides of the outlet, and the GFCI will NOT activate. That is what a circuit breaker is for.