My answer: no, not in its original form.
As it is, the thing (probably) won't pass the NHTSA crash tests, not to mention the basic FMVSS standards. Once you add the airbags, mass, 5mph bumpers, and so on, the puny 33HP engine won't do at all. NHTSA will require stability control, so ABS will be required.
Americans also won't buy vehicles without radios. They'll want an automatic transmission.
Tata will have to go for a much larger motor, which will reduce the fuel efficiency and raise the price.
By the time the missing features are added, the car will cost $5000. You can buy a nice used Chevrolet Cobalt, Saturn Ion, Ford Focus, etc. for that kind of money. And you'll get a proven product, with wide dealer support.
Does America Want The Tata Nano? You On Here » industry » Does America Want The Tata Nano?
