2002 Volkswagen Polo catalytic convertor

2002 Volkswagen Polo 87000 miles

Hello, my mechanic told me that I need a new cataytic convertor. He told me that it would do nothing to the car if I didnt buy one right away. So I haven ´t replaced it yet. I can feel there ´s something off with the car though. The idling is low and sometimes it ´s shaky. Could this be due to the cataytic convertor. Is it dangerous to drive around with a bad convertor and can it damage the car? Could this be causing the car to shake sometimes? Thank you in advance.

Helia