A typical 14 second car is in the 10-11 pounds per horsepower range. so a G body would need about 300 horse. Like a stock GN. But the physics completely defy the ability to get 35 mpg in the city.
However, is any car capable? Absolutely. I think everyone has overlooked the key component. Nitrous Oxide. The important difference between nitrous and turbocharging is that the nitrous doesn't affect how the engine consumes fuel until you push the button. With ANY boost, an engine needs more fuel.
In my opinion, the best car to start with would be a pre-70s beetle. Those cars weighed less than 1800 lbs and were rear wheel drive, making them good at the drag strip. Of course, the stock engines were garbage, but the performance aftermarket is huge for them.
From a pure numbers standpoint you need to get 180 horsepower at the strip for a beetle, but keep air/fuel consumption under 4000 liters/min in the city. You also need about 100 ft-lbs from the engine to make the car driveable at low engine RPM in traffic. So you would probably need a 2.0 liter engine or so. That should make 100 ft lbs with natural aspiration. The cam would be a limiting factor. One that maxes out around 4500 rpm would be necessery for low RPM driveability. However, if you dumped enough nitrous and extra fuel into it at the track, you could theoretically boost your torque to 200 ft lbs. 200x4500/5250=171 horsepower. Not far from what you need.
So basically, a stock 1968 beetle, with a 2.0 liter VW air cooled pancake 4 cylinder, stock gears, computer controlled nitrous/fuel injection (4 injectors, 1 per intake manifold for city use, 1 per manifold for nitrous guzzling)
Not only would this probably work, but it would be relatively easy. The hardest part would be driver restraint. You couldn't shift past 2000 rpm in the city or your mileage would drop...