The IEEE recently looked at this issue. The sky line would be filled with the multi-kilovolt lines required for this. And exactly when you want the electric cars the most (high heat, high smog days) they can't be used because the air conditioning needs it 24/7.
But they're hybrid, remember?
I don't know what the IEEE looked at, but here's my BOTE calculation. I don't know the exact difference between our family's peak day and nighttime electrical power usage, but just glancing around, I see more than 1000 watts in lighting alone. Add in microwave, refrigerator, computers and monitors and it's probably much more, but let's say 1500 watts conservatively. Over an eight hour night, that makes 12,000 watt-hours. That's 40,800 BTUs. There's about 100,000 BTUs/gal of gas, so that nighttime electrical power difference is equal to about 2/5 of a gallon of gas.
I live about 10 miles from work so the commute is 20 miles. Let's say a hybrid electric auto gets 50 miles/gal. My 20 mile commute then takes 2/5 gallon of gas. On a typical day I'd consume no gas at all. Overall I expect I'd get 3-400 miles per gallon. There are a lot of people like me. With no grid upgrades at all, we'd achieve a huge reduction in gas consumption.