Technofreak:
Yes, this is a possibility.
I have based my expectations on the fact the heat pump we have installed uses 30% less power than the old heater and produces up to 2.5 times the amount of heat.
I suspect where people have experienced a much larger bill than expected is where the heat pump is spending a significant amount of time defrosting. Our unit has rarely needed to defrost. I think the other issue is the one mentalinc talks about in his/her post. That is the disparity between the temperature set on the controller and the actual room temperature.
In our case a temperature setting of 18 degrees gives about 23 degrees room temperature. That is because the temperature sensor is in the unit which is mounted on the floor. The temperature measurement is taken from the air being drawn into the heat pump and when the room temperature is 23 degrees the air temperature at floor level is 18 degrees.
In this case if you were purely setting the desired room temperature by reference to the setting on the controller you would be attempting to achieve a room temperature of around 28 degrees and as such wasting a lot of energy.
Heat loss increases with the area heated and the temperature difference. It'll be interesting to hear how it goes.
We find even with the high wall models it gets a bit hotter than we set. A setpoint of 21 gives 22 to 23 with our Fujitsu, but it takes a setpoint of 20 to get there with the Daikin.