And when are most people going to be charging their cars? At night. So you'd have to factor in ADDITIONAL infrastructure to store that energy for later use including the impact of birth/care/disposal for that storage.
http://cleantechnica.com/2014/02/03/grid-capacity-electric-vehicles-actually-problem-studies-find/
"In fact, Navigant says, the power grid we have right now can sustain millions of electric vehicles without anyone having to invest in new power generation."
Most EV owners charge at night when there is less demand. Right now, the grid has a great over capacity during most times to be able to handle the few days where there are spikes in demand. If there is a large increase in EVs, then power demand may actually become more stable throughout the day. It's also possible to use the EV batteries as a distributed storage mechanism, to help meet peak demand. I believe they are looking at that in a program with PG&E in San Francisco.