There will be a voltage drop across the regulator. This voltage drop times the current through the regulator is converted to heat, raising the temperature of the regulator. If the load has a low impedance, then the regulator may reduce the output voltage further, so that the output power will always be less than the input power.
The National/TI specification says the recommended operating condition is when Vin = Vout + 3V to + 40V. Any outside this range and you are on your own.