From Tesla's website it looks like they take ~1 Hr to charge (1C rate). That would make me think they are limited by the maximum charge rate of the cells.
On the contrary, it is limited by the size of the cable going from the electricity distribution grid to the side of the car. With a typical (not a high performance) car engine capable of generating 75kW of mechanical power or so and a typical wall socket (in the UK at least) capable of transferring 3kW (and the average house having a 24kW total limit), there's going to be a problem that can only be solved by upgrading the cabling and using special high power sockets.
At some point the amount of copper needed to carry the current becomes heavier than the batteries themselves. 120kW is already outlandishly strong, at 120V it's 1000 amps!
If you had batteries which could accept that (Li-Ion's don't like going above 3C I think) and had the kind of energy density being claimed then it would be a relatively trivial matter to use a larger bank of them to provide the peak capability to charge a smaller bank of them.