I am a huge advocate of listening to your body. I had a cold for the past three days and since my body was telling me not to work out, I didn't. I feel much better today so I did MM. I think if I had pushed myself to work out when my body was asking for rest, I would still feel run down. Sometimes when I have a cold, I feel like working out anyway, so I listen to my body and work out (but not too hard).
I think it's unhealthy and counter-productive to push yourself unnecessarily.