> Recharging in the same time as a gas refill is unlikely to ever happen.
Agreed, but only because it is unnecessary, not because it is impossible. A 15 minute recharge every 4 hours (250 miles) is about as good as anyone really needs.
> To go NY to Florida in an electric car will take on the order of 1MWh.
Tesla Model S goes 265 miles on 85 Kwh for 3 miles/kwh, so the trip from Orlando to NYC (~1000 miles) would take about 333kwh which is about $40 worth of power (nothing unsustainable about that for the occasional long trip). Break this up into one 15 minute recharge every 4 hours of driving (250 miles) leads us to a recharge power of 333 kW (with a battery sized ~85kWh). The existing Tesla superchargers are already outputting 90 kW, so we are not that far off from the "plenty good enough" point. No laws of physics need to be broken to output 4x that current.
> Now think of how many people are fuelling up at a gas station at any given moment, and think about it if they are all drawing a power of 12 megawatts.
The instantaneous draw is irrelevant because there are energy storage elements in the grid and at the charger (batteries, capacitors, etc) to smooth everything out to the average demand. The average demand is less than 40 miles per car per day, which is 15 kwH per car per day; and overwhelmingly people will choose to charge low and slow from their home outlets at night. There really aren't enough people driving 1000 miles in a day to generate a gigantic continuous supercharge demand on the grid. Pretty much every study that has been done on this has shown that the existing grid and generating facilities can easily keep up with increasing power demand from electric vehicles.