The "pulse" of an Electro Magnetic Pulse acts like a massive power surge; it essentially burns out the circuitry of printed circuit boards; pretty much any sort of electronic device- a laptop computer, a TV, a clock radio, a cell phone, etc, that is not shielded properly against an EMP will be fried;
In a vehicle, that would include the cpu and modules that run the fuel, electrical, and ignition systems; pretty much everything that regulates the fuel and spark to the engine.
As a result, most cars made in the last 30 years would be incapacitated immediately, just like everything else electronic.
Or at least , that's the theory.