It is doubtful that he can do that, provided that you are not stationary on the sidewalk. In other words, you have to keep moving. If you are sitting on the sidewalk, say in a lawn chair, holding up a sign, then it is possible that the city could begin to start charging you "rent" for the space.
Knowing small town Texas mentality -- do you really think that you are doing yourself any good? Unless you are able to get a significant number of other people to join you in your demonstration on a regular basis, it is doubtful that you are going to be successful in changing anything. The only place that you are going to accomplish any changes is in Austin.