Q: My car is shaking.

Hello. the Diagnostic Trouble Codes would have to be retrieved to begin the diagnosis. Unless the shop retrieved all codes and performed a diagnosis and tested the coils (there are six of them on your engine), what they have told you is pure speculation. Although a coil defect can cause a misfire, there are quite a few causes elsewhere in the ignition and fuel system.

As far as the consequences though, they are giving you very good advice and actually engine damage is just the beginning of the concerns if the engine is misfiring. If the misfire(s) result in unburned (raw) gas entering the catalytic converter, you can destroy the catalyst in very short order.

I would be ashamed to find out that your only issue is caused by a mere faulty spark plug wire (not that costly) but you continue to drive the car causing hundreds of dollars of damage to the catalytic converters (converters are not repairable; the factory OEM converter on your car could easily be $500).

If I were you, I would not drive the car if it is actively misfiring. A mechanic of your choice or YourMechanic, if in your city, could quickly diagnose your Check Engine Light and get it repaired and reduce the chance of further damage. Unfortunately, engine misfires in modern vehicles are not as inconsequential as those that might have occurred in older vehicles prior to the 1970’s.