Keep in mind that what matters is not just the amount of power generation capacity, but the ability of that capacity to respond to demand.
Some background: The bulk electricity market (at least in NY state) is run as a giant linear programming problem to satisfy the demand for all regions with a set of supply curves that suppliers bid into the market. They all get paid the same price that the marginal watt (the last watt you need to buy to meet demand) costs.
So, natural gas turbines, who can turn on and off relatively quickly, will bid high and are likely to be the marginal watt. Nuclear plants bid very low and occasionally negative because it actually costs them money to shut down because they then can't start up again soon. So, they want to be sure that they are going to be scheduled.
This is oversimplified and ignores the difference between the day-ahead market and real-time market, products like regulation (we pay money for people to be ready to turn on/off and keep things at 60Hz), and inter-zone transmission)
The point is that a nuclear plant can't suddenly turn on in response to a spike in demand from quickly-charging car batteries. A bigass flywheel or a bigass battery (shameless plug for Sadoway: http://www.ambri.com/) might though.