It may actually be possible to make a car with a smallish I4 and fast acceleration, all you need is a decent size electric motor and a battery pack that can deliver the (burst) current. You won't have the sustainable top speed you would normally expect from a car that accelerates fast, but top speed is not an issue if the car can go as fast as you need.
These batteries could probably do the job:
http://www.a123systems.com/html/home.html