Tim,
Shoot back with "so you're physically handicapped with a bum leg that might need to be amputated soon, too?"
On a side note: A ray of hope has touched my club here in NC. Due partly (probably mostly) to a less-than-stellar financial situation of my semi-private club, the club seems to be more willing not to anger anyone with strict rules. The result? They seem to have relaxed, almost gotten rid of the mandatory carts rule before 2:00 on weekends.
I joined up with one guy walking late in his round around 2:00 a few weeks ago, and asked if he'd been walking the whole round. He said he'd tee off just before noon and that no one said anything to him about having to take a cart. This past weeked, I noticed 3 guys (father and two sons) carrying on the 9th hole around 12:15-12:30, having started probably around 10:30. I ended joining up with the same guy from the first time and he believes that they don't want to piss off anyone. I said to him and firmly believe that if they simply had no mandatory cart rules, most would ride any ways, and those who want to walk can have more freedom in when they play.
Hooray for my club, sort of. I just hope that if, for whatever reason, the club does better financially that they won't go back to the old way and see that the way it is now keeps more people happy. It's been proven by the NGF that walking and riding has virtually no difference in pace of play of a foursome (it was 4 minutes difference over 18 holes).