Tesla will begin to crack the mass market when the Model 3 enters production. Starting at $35k before government incentives, it will likely have a total cost of ownership comparable to a mid-range Ford Fusion or Toyota Camry. At that point, I think Tesla is really going to become a major player in the auto industry globally.
Long-term, I don't think there's really any doubt that BEV's are the future of the auto industry - as battery production scales up, costs will fall, and range will continue to improve. Moreover, even the most efficient IC engine theoretically possible doesn't even come close to matching the efficiency of the all-electric powertrains currently on the market; IC engines' obsolescence is merely a matter of time.