Several more readers sound off:

Football will not disappear because of the risk of brain injury.  Simply put: there's too much money on the line for players and team owners to just hang it up because of concussions.  Instead the NFL has been addressing this through rule changes to avoid some of the riskier scenarios.  Kickoffs have been altered to limit the number of returns.  Rules have been implemented to penalize players for dishing out hard hits to player's heads when they are exposed.  Players who receive concussions must be evaluated by third-party independent doctors to clear them to play again after receiving a concussion.  These rules make the sport safer if not completely safe.

As a fan of the sport, my feeling is that as long as the players are informed about the risks and the NFL does it's best to mitigate those risks, then I don't have any qualms watching it.  Brutality is a side effect of the sport, not the point of it.  It's not like boxing, UFC, etc, where the point is to inflict injury and defeat an opponent by physical attrition (sports I do not watch). I've seen games filled with injuries and I've seen games where everybody was fine save a few bruises.

Another disagrees:

My cultural capital here: Chicago Bears season-ticket holder, and someone who writes about sports for various publications (and teaches sports lit). My prediction: football as we know it will be done within 15 years.

As evidence emerges, and it is constantly emerging, that CTE (chronic traumatic encephalopathy) does not just occur at the game’s highest (and most brutal) levels, the NFL and NCAA, lawsuits will continue.  The science is there, and it will come out in court; not just whether the NFL or NCAA lied to their players or hid the risks, but the pure fact of the risks.

This will lead insurance companies to refuse to provide liability coverage for football leagues and players, since they know they will have to pay out too much.  And as soon as school districts are unable to get liability insurance, they will be forced to drop scholastic football, even if parents would allow their sons to continue to play.  Without the flow of grade school players to high schools to college, the NFL withers and dies.

I predict that it will be transformed into something like flag football, with an emphasis on the passing game, speed, and hands-skills.  But the day and age of gigantic defensive players obliterating receivers, quarterbacks and running backs is soon to be over.  And I’m OK with that.

Another is on the same page:

The way it will happen is by losing its feeder program. Football is big money and the NFL has deep pockets. The same with college to a lesser degree. The weak link is high school. There are already yearly budget battles in most school districts across the country. It isn't a very big leap to see that a few lawsuits could start a cascade of high schools ceasing their football programs. They simply wouldn't be able to afford it.

Another:

I have no idea if football is going away. But to anyone who says that football is too big to fail, I would point out that the most popular spectator sports in the early part of the 20th century were boxing and horse racing. I am sure that the idea that those sports would be seen as fourth-tier entertainment in 2012 would have seemed as crazy then as the idea of football going away does now. Things change.

Another:

The sport probably won’t literally disappear, but it could easily end up like boxing – once among the country’s favorite pastimes, now relegated to the fringes of polite society due almost entirely to the obvious toll that it takes on its participants.  Even sadder, absent an outright ban and assuming some level of continuing popularity, the only people who will play football will be the same people who continue to box (and, for what it’s worth, join the military): the poor and otherwise dispossessed who don’t perceive any other options and can’t afford to worry themselves about things like brain trauma.

Another notes:

This isn't the first time football's injury risk has risen to the level of national discussion.  Over 100 years ago President Roosevelt was faced with a movement to ban the game based on the rising number of injuries (and deaths!) at the high school and collegiate levels (pro football was only in its infancy at the time).  As this article points out, Roosevelt interceded and was able to convince the football powers that be to institute badly needed changes that saved the game.

Would Obama step in at this point?  Doubtful based on the political costs, as well as the other external pressures the NFL already faces to clean up the sport.  In fact, despite that fact that it's coming too late, the current NFL Commissioner's signature issue is safety in the game.  It's one of the reasons he came down so hard on the Saints during the recent "Bountygate" scandal

The NFL will clean up it's image and improve the safety of the game.  This time around it won't be a meeting with the President that does it, but the effect on the bottom line.

Earlier discussion here, here, here and here.