How many kilowatts (or amps) can I safely draw from the AC grid?
Here in Belgium a house has a main automatic switch (before the fuse cabinet) approved by the electricity utility. The switch's rating is the maximum you can draw for the whole house. For my apartment that's 40A (at 230V).
I guess in California things will be more or less the same. I wouldn't worry about the wiring outside the house. It's the wiring inside the house which will be the limiting factor. You can't use the standard wiring, that's not up to the high currents you need. Rewiring (even if your landlord agrees) will be cumbersome, since the tubes for the wires may be too thin for the thicker wires, let alone that you can pull them through. My guess is that you may need at least 6mm\$^2\$ wires, I once installed a 3\$\times\$19A heater which required already 4mm\$^2\$.  

I mention the 3\$\times\$19A because 3-phase is the way to go for this kind of power, really. If the utility supplies it, and the landlord allows for the required changes you get 3\$\times\$208V instead of 1\$\times\$120V, which makes a world of difference: the 72A will be reduced to 13A per phase.