Why cannot we work in millivolt range
Even if you could design logic circuits to work at sub 100mV logic levels, power supplies that feed the logic are usually quite noisy and this noise will also appear superimposed on the logic signals - getting a logic supply that doesn't produce noise that could turn a 0 into a 1 or a 1 into a 0 would be fairly tricky. You'd be looking at about 30mVp-p noise maximum and probably more like 10mVp-p for decent reliability. 

It's not just noise but power supply accuracy too - producing a power supply whose voltage drifts up and down (say) +/-0.25 volts under all load and temperature ranges isn't that hard but doing so (and keeping spurious noise) to below (say) 20mV maximum is a big challenge.

But, as has been mentioned by @PlasmaHH, transistors inside logic gates need a certain voltage to turn on and if you can invent a transistor that can turn on and off reliably with a 100mV range of input voltage then you should become very rich. I'm not saying it's a laws of physics thing but it very well might be.

Remember, the beauty about digital solutions is that they avoid digital corruptions by have a distinct "voltage gap" between high and low. Currently some chips use 0.8V as the logic supply voltage so things are moving this way.