does it take more energy to lower the temperature of something as you get closer to absolute 0? Instinctively I would assume it would take exponentially more energy to get from 0.01 to 0.001 (Kelvin) then it would to get from 2 to 1 (Kelvin). Otherwise it seems like it would be quite easy to get to absolute 0 which I know to be impossible.
At the same time I don't see why it would be more difficult since the former increment is a minuscule  fraction of the latter. 
So if it is the case, then why is it so? And if it isn't then why is it such a great achievement when we get a fraction of a degree colder?
 A: the efficiency of an idealized refrigerator using a carnot process is (according to wikipedia, I have the correct derivation stowed away with my notes in the attic) The carnot cycle is the most efficient cycle for 2 heat reservoirs.
$$ \frac{Q_l}{W_h}=\frac{T_l}{T_h-T_l}$$ 
now as the surrounding area stays at more or less the same temperature, the amount of heat you can extract for a given amount of work will decline.
The problem isn't really that you need to extract more heat for the last few degrees (the inverse is true) it's that it's more difficult to do so.
A: It takes an infinite amount of energy to pump all heat energy from an object to a warm environment using a heat pump. 
Let's say the cooling is done by a Maxwell's demon. To reach absolute zero, the demon must go trough the work cycle infinite number of times. As each cycle requires the same non-zero amount of energy, the total required energy is infinite.
A fundamentally different way of cooling:
In empty space make an arbitrary long cylinder with a piston, put some gas in the cylinder when the piston is down, let the gas do work by pushing the piston. This way of cooling the gas only takes a limited amount of energy, no matter how much you cool the gas. Note that all heat energy that disappeared was converted to mechanical energy. This device is not a heat pump, it's a heat engine. 
