Energy use for cars is substantial, a significant percentage of the energy usage of homes. If that energy use shifts from fossil fuels to home electricity supplies we'll need to substantially increase the energy delivery possible to homes.
The total energy usage shouldn't be much of an issue as we'll move electricity use from refineries to charging batteries – I believe these are at least in the same ballpark. But "last mile" electricity delivery is not capable of supporting an electric car in every household (or even half of households) in many areas of the world.
It will be interesting to see what the solutions to this are. Smart grids where cars cooperate to ensure they don't all charge at the same time, and increased use of public fast charging infrastructure (at sites with better grid connectivity) are the most likely I suspect.