The 3 will be a market changer for the low-end of electric vehicles. If they hit $35K with 200+ mile range, it means all the other electric vehicles in that range, such as the Nissan Leaf, will also have to hit 200+ miles or drop below $25K.
Right now there are a number of cars with 80-100 mile ranges in the $30K-$35K range. They won't be able to compete with the 3 without some major improvements.
This also will shake up the used market. Right now 80%+ of Leafs are leased, so about the time the Model 3 comes online all the Leafs on the road today will be for sale. That's a lot of cars, all with 80-mile-ish ranges. Now if new cars at $35K have over double the range, the price of the used cars will be much lower. So if a 80-mile range is sufficient (perhaps for your second or third car in the family), then you'll be able to go electric at a fairly reasonable price in two or three years.
I think the long-term impact will be that most people who have a good place to charge their cars at home will consider electric cars after the Model 3 has had a couple of years to shake up the market. I would guess in five years it will be typical for families with more than one car to have at least one electric, and in ten years the majority of new cars will be electric.