First, the losses in the cable reduce the overall available power to load (as pointed out in the prior post). Second, the power goes to heat and too small gauged wire can be a fire hazard. The provided link gives you the resistance of various gauge wire over 1000 feet. Nominally, at 2000 watts the maximum current would be about 18 amps...round up to 20 amps.
Anything larger than 16 gauge will handle the current, but the resistance is 4 ohms. This means that the voltage (V=IR) would be reduced 80 volts across the cable and the power dissipation would be (P=VA) 1600 watts. Not a good day.
0 gauge has a resistance of .0983 ohms for 1000 feet and the voltage drop would be 2 volts, power loss would be 40 watts.
Clearly, you may not need 1000 feet and the numbers reduce proportionately with reduction in length.
I absolutely agree with the prior posts regarding the hookup. I had an electrician install a manual transfer switch. The switch allows me to decide what distribution to power. In addition, it guarantees that I will not back drive the grid and create a hazard for line crew etc... I picked up a 6500 troy built generator for about $900 which will keep my house reasonably covered.
http://hyperphysics.phy-astr.gsu.edu...es/wirega.html