I'm no electrical engineer, but I think we can do some napkin math.
80khw battery in an average model s * 300000000 million cars / (3,911,000,000,000 kwh energy use in the in all of 2015 [2] / 365 days per year) = 2.239 times as much storage in cars on the road versus energy usage which seems pretty doable. Also, it also gets better because as car batteries age and their storage / weight goes down, you can replace them with new ones and put the old ones in grid storage locations where weight / storage does not matter and run them till they are literally dead.
[1]: about a little less than 1 per person (just rough estimating here)
[2]: https://en.wikipedia.org/wiki/List_of_countries_by_electrici...