Thank you so much for your help. I will be asking these questions. you seemed
very knowledgable and you were most helpful. Thank you.

The short answer is "no" - your car will do just fine without the catalytic
converter working at peak efficiency. In fact, the emissions are probably
not much greater than they were before the light came on.

The long answer involves knowing what "codes" are being seen by the shop
when they read them. Although the codes are specific, they aren't always
clear and don't often point right to the specific problem... that's why the
shop has danced around things like this. In fact, replacing the catalytic
converter may not be the solution, and that's a good reason for them to
evade it for so long. If you can find out what the codes are (they will be
in the form of a "P" followed by 4 digits, like "P0452") and relate them
here, we can confuse you more <8^P

There are two downsides I can think of in having the light on, other than
the distraction. There is a small risk that another problem that would
normally turn on the light will now be missed, and I don't believe you can
legally sell a car in the US with the "check engine" light on (not sure
about that.)

Mike

My engine light has been on for months. I have taken the car in several times.
Honda has fixed things several times. The light always comes back on after a
day or couple of hours. My 2000 Honda Ody. is at the shop again now they say
it is the catalytic converter. Actually they have told me that it could be
that from the start, but because of cost we tried some other things it might
be. Anyway, my question is what happens to my car if it is not fixed. Cars
did not use to have them. I know it is for pollution control. But does it
have any effect on the car its self?