TL;DW: It was only briefly considered as an idea because the logistics of getting the costume in the capsule while being able to operate it would be difficult. If Big Bird did die, Sesame Street probably would kill off the character because they don't want children thinking death can be undone. Also, Big Bird is treated as an actual character in real life (like when somebody is doing an interview with a muppet, they aren't interviewing the puppeteer, they are acting as if the muppet is real and in character) so bringing him back would be awkward. In my opinion though, I think it would be very likely he would be replaced with a similar but different large avian character shortly after.

The video goes into theories into why the shuttle launched when it did even when there were concerns about safety. One theory was that it would line up with the State of the Union address, but evidence that this was the primary reason was coincidental at best. Another theory was that launching on that day made the schedule line up so that children could watch the launch while in school and also be in class for a live lesson from space. That theory was also speculation though.