i assume you are starting with a positive supply? if so, something along the lines of the following could be used... this creates a "floating ground"
of course, this contains an extra LED and Resistor to tell if it's powered, and the overall circuit will need to be slightly modified to accomidate 12 volts.
Look for a charge pump IC. You should be able to find one that will give you a negative voltage equal to the positive voltage input.
plot - I don't think you can assume that OpAmps draw the same current from both rails. For example: an opamp driving 25mA into a load will be drawing those 25ma from the positive rail.