Q: Rough idle, seems to misfire but never dies and no Check Engine Light.

When stopped at a light or idling, it seems like the engine wants to quit or it seems to hesitate. It feels like it is misfiring but it is random, not rhythmic. Sometimes, it won't happen at all even when I listen for it but the next time I am stopped at a light, it will happen. Sometimes it is more severe than others, even making one think the engine will die but it never does. There never has been a check engine light and I don't think the mileage is worse than before although I haven't checked it. It started happening after I tried to repair the AC/heater blower motor switch because it wasn't working in all four speeds. It ended up with only the two fastest speeds but then we noticed this hesitating or maybe misfiring. In fact, it wasn't happening when the fan was off. But then it started happening all the time, fan on or off. I replaced the blower switch with a new one but it did not completely get rid of the hesitating. It seems to have reduced it, I think.

My car has 220000 miles.
My car has an automatic transmission.