Possible catalytic converter

Try removing the catalytic converter and see what happens.

A plugged exhaust system will cause an uncommonly smooth idle with seriously reduced engine power. You'll also hear a steady hiss from the tail pipe instead of the normal "putt putt" sound.

What you're describing is a cylinder misfire. Start with spark plugs and wires, and have the diagnostic fault codes read and recorded. The people at many auto parts stores will do that for you for free.