If you were in school, it is very possible you did watch it live:
"With Christa McAuliffe set to be the first teacher in space, NASA had arranged a satellite broadcast of the full mission into television sets in many schools, but the general public did not have access to this unless they were one of the then-few people with satellite dishes. What most people recall as a "live broadcast" was actually the taped replay broadcast soon after the event."
http://www.nbcnews.com/id/11031097/
"With Christa McAuliffe set to be the first teacher in space, NASA had arranged a satellite broadcast of the full mission into television sets in many schools, but the general public did not have access to this unless they were one of the then-few people with satellite dishes. What most people recall as a "live broadcast" was actually the taped replay broadcast soon after the event." http://www.nbcnews.com/id/11031097/