Weasel words from NASA hierarchy:

Could anything have been done to save the astronauts, if not the shuttle, had the problem been identified earlier?
If you look realistically at where [the shuttle] was it didn’t have many options going for it: a very limited duration, few consumables, no ability to go to the [space] station or do repair and limited ability to even do any type of inspection. We would have had to rush to launch the other vehicle [shuttle] on the ground and that would have been a risk for that vehicle. Even if you knew for sure that you had damage on the first that made it not recoverable—and I’m not sure how you would do that even with all the imagery you thought you could get—it would still be a very tough management decision to launch a second vehicle with exactly the same kind of external tank and the same likelihood of that kind of problem. So it made for a very difficult decision. Conceivably could something have been done if we’d known such-and-such information on such-and-such a date? Well, yes, but when you look at all the things that would have had to happen to make that possible the chances of it making a difference is remote in my opinion.

There has been plenty of reporting that NASA staffers suspected strongly that the foam caused the problem. If the NASA mindset had been proactive instead of staid and apparently discouraging of dissent in the ranks, a rescue mission could have been mounted that might have saved the astronouts and Columbia. Had that happened, NASA would have been seen as heroes a la the NASA of Apollo 13 days. Instead, they sat on their thumbs, ignored the problem and hoped it would go away, and are grounded, maybe for another year, maybe forever.

Gene Kranz, well-known former flight director, responded to the following question as follows:

Q: After a while, the public came to see the success of the space program as inevitable, but you paint a different picture of facing constant risk and danger. How did we get through the program without more disasters? What were the guiding principles?

Good question, one that is difficult to answer briefly. The "human factor" was the key when all of our glittering technology broke down. It was people working with the knowledge and very primitive technology at hand that controlled the risks of our work. We knew there would never be a second chance, so our personal readiness was extensive. The spacecraft and the technologies were fresh from the laboratories. There were no books on our jobs, no manuals on the systems we would fly. We learned our job and then taught the rest of our teammates. We were engineers and scientists flying a spacecraft that moved five miles a second, with a communications system that dated back to the Old West and the pony express. We succeeded because we were a team. If one of us did not have the answer, we searched for the teammate that had one. The cumulative experience of our training and our missions was additive, and with each successful escape we gained the confidence to walk closer and straighter on the edge. We became a team, experienced and unafraid to make time-critical risk judgements in front of the entire world.
The principles of flight control were often simply expressed: "If you don't know what to do, don't do anything! Learn to say I don't know, then go find an answer! Dammit, there are no books; use your judgment! You better be right the first time; you don't have a second chance." We got through the flight program because of the human factor. We were a brotherhood and when times got tough and our equipment broke down, we stood together. When we won it was everyone's victory.

My sense is that this esprit de corps, or cameraderie, that was prevalent in Apollo days doesn't exist any more at NASA. Look at that last paragraph; nobody running the show said that during Columbia's last mission. Without that team spirit, that brotherhood, manned space flight is that much more dangerous. As Apollo 13 [the mission and the movie] exemplified, the real stars at NASA were the guys on the ground, who refused to consider failure as an option.