Possible Exhaust Back pressure on 96 Olds Cutlass Supreme

1996 Olds Cutlass Supreme, thought it had a rough idle but further investigating leads me to believe that the car/engine shaking is caused by back pressure in the exhaust. Looking at the exhaust from under the car, the exhaust pipe shakes bad. At the end of the exhaust pipe there is not a free flow of gases, the exhaust comes out inconsistently. What can cause this? I am not having any check engine lights come on. I changed spark plugs, wires, mass airflow sensor, and fuel filter.

Possible its the converter clogged, especialy if its the original.
How many miles on this 3.1 ?
Could also be a muffler issue, clogged or something inside came apart adn blocking the exhaust.

Yes, it is a 3.1 and there are about 143,660 miles on it. I was thinking possibly a clogged catalytic converter too. Someone suggested that I just knock out the core and not even worry about replacing it. My concern about that is wouldn't that cause problems with the sensors?

knocking th ecatalist outa the converter isnt that easy.

It would affect the sensors if it has a O2 sensor after the converter.

if I change the converter will i have to replace the O2 sensors also? there is an awful smell after I drive. I have heard that if the cat is bad it can smell like rotten eggs. I can't tell if it smells like that but it sure does smell bad.