Did you have a power-on LED on that Boarduino? If so, I'd guess that 3mA is all being used there, because according to the datasheet an ATmega328P in power-save mode (which I'm assuming is what's being used when in "deep sleep") pulls a few microamps.
My *guess* from looking over the Arduino Micro schematic on arduino.cc is that you should be able to get sleep current in the uA range if you desolder the power-on LED, and the same if you don't solder in the same LED on a Boarduino. I've not tested any of this though, so hopefully some smarter, more experienced and better looking commenters could confirm or refute that conclusion?
If you're really going for power savings, explicitly set any unused pins to digital inputs and enable their pull-up resistors. (See 14.2.6 of the complete datasheet here