Reasonably quickly, but not as fast we'd like.
US pure EV sales have doubled each year for the last three years (from a very small base) and pure EV and PHEV sales are growing faster than hybrid sales did when they were introduced . Tesla has a large backorder book. Nonetheless, PHEV sales aren't growing as quickly as many people had hoped.
Cost isn't the problem.
Hybrids, EREVs and EVs are already the low cost choice for Total Cost of Ownership (per Edmunds.com), so if cost were the driver....we would have reached the tipping point. Buyers of new light duty vehicles (cars, pickups, SUVs) sales just don't seem to be very price sensitive. The minimum cost US vehicle is about $11k, while the average vehicle is more than $30k. The average new car gets about 25MPG, while 55-100MPG vehicles are available. New car buyers just aren't paying much attention to minimizing costs.
Supply isn't the problem: Toyota, Nissan, Ford and GM will tell you that they could double production of their hybrids, EREVs and EVs literally overnight, if demand were there.
There are two big problems:
First, the vast majority of people are very slow to move to new things. Individual consumers have to see people around them using this new thing for quite a while to become comfortable with them. For example, online food ordering has overwhelming benefits for parents, but Webvan went bankrupt: they counted on people moving to a new thing too quickly.
Commercial users of heavy duty vehicles face large problems of economy of scale, long-lived investments and operating in a tough competitive market. Large fleet customers have been experimenting with pilot programs, but have been afraid of being first movers ("Pioneers are the ones with arrows in their backs"). That suggests that the early rate of adoption may be deceptive. At a certain tipping point fleet buyers will decide high oil prices are permanent, and that electrified/alt fuel vehicles are clearly cost justified. Then, sales will grow quickly.
Second, the primary reason for EVs is external costs like Climate Change and the cost of military conflict in the M.E., and as a society we haven't prioritized dealing with those costs. We just haven't. Until we do, with things like carbon and fuel taxes (which even the most conservative economists support for external costs) and acceptance by Republicans, it's unrealistic to expect fast movement by consumers.