I've been thinking about this question ever since a talk with one of the judges at Atlanta.
Our principal encouraged all the teachers to show their students the Championships webcast. After every match, every team member's cell phone (including mine) was full of text messages either congratulating us or telling us not to be discouraged. Our principal called our mentor telling him how proud he was for bringing such a program to the school. When we got back home after the championships, we were bombarded with students asking us questions about the trip, asking us how we built the robot, and of course the stereotypical battlebots questions. There is a massive amount of students wanting to join next year's team.
We talked to one of the judges about how much the school's administration and the students are supportive of us, and his answer shocked me. He told us that until recently, his school's principal didn't even know there was a robotics program. Students came back home after competitions like as if nothing happened. This saddens me.
So, as the thread title states, how much does YOUR school's population care about your team?