I don't see the big 3 going after this market. They'll let Elio have the small market share that will be. With a small price comes a small profit margin which is of little interest to them. I see very little margin in this vehicle at this price once established I would expect a price increase.
Small margin? I don't think a 15-20% margin is too bad, actually. In fact, compared to most cars it's very good from what I've read. Now, maybe with the traditional "dealership" model that other manufacturers use, that margin is cut into. But for Elio, that would be a comfortable margin I believe as they do not have such expenses.
That said, this assumes they are able to cut their costs a bit more and achieve that $1,000 profit per vehicle that they have planned. I do suspect the price will rise after a year or two, if for no other reason than inflation and demand and other costs.