There are two things I can see the anti-gun groups, the media, and the politicans pushing out of this.  The first is another law limiting magazine capacity.  The other is stricter mental health screening for gun purchasers.
Magazine Capacity Limitations
They tried this in 1994. Even if they removed grandfathering, there are a lot of magazines floating around out there that exceed ten rounds, and virtually all magazines exceed five. Magazines are currently completely unregulated. There is no way a law banning them will have even minimal compliance. Magazines exceeding the limit will continue to be common and available, even if Congress bans them.
It also doesn’t take long to change a magazine. As this killer must have done several times while he was systematically executing his classmates. Would it have really made a difference if he had needed to carry three ten round magazines rather than two fifteen round magazines? I doubt this would have altered the end result. In fact, I can’t really see any situation where magazine capacity limits would save lives. Magazines are just too easy to change.
More Mental Health Screening for Purchase
It’ll inevitably be proposed that gun purchasers go through more rigorous mental health screening.  Except proposals requiring physician signoff, references, or making anyone who’s had mental health treatment a prohibited person. This one could be the one we have to worry about the most, because people will more easily see the relationship between the current tragedy and the proposal.  But keep in mind that millions of people are treated every year my the mental health profession, and only a small fraction of them are truly dangerous. Ever taken anti-depressants? Want to be a prohibited person because you one saw a psychiatrist? Do you want your neighbors being consulted and asked if they think it’s OK for you to have a gun? I Don’t either. This is a massive invasion of privacy, and we can’t stand for it. I would also note that Canada does have these strict requirements, and so does Massachusetts.  But it didn’t stop mass killers from committing their acts there.
People who want mental health screening really want guns banned.
You can bet that any proposal they make will cover
anyone who ever had marriage counseling,
anyone whose child was ever given psychological testing (can’t have guns in the house with crazy people)
anyone who has been involved in any loud argument that resulted in a police report (violent crazy)
anyone with an arrest for drunkenness in college (unstable0
anyone who has seen a psychologist, psychiatrist, social worker for situational depression after losing a loved one or been prescribed anti-depressants by their family doctor.
In other words, probably 75% of the population.
In Mass, the cities that want a doctor’s note usually don’t issue many permits. It’s not because their standard is high once they have that note, but because the doctor doesn’t want to be responsible if something does happen, even 40 years down the road.
I imagine it’s much the same way the judge in the Virginia Tech case is now wondering about his own approval of outpatient treatment.
I was under the impression that the mental health community is opposed to most of these laws because they (1) serve as a disincentive to seek help and (2) they don’t want to be out in the position of arbiter for such things. The result is the same community preferring a flat ban so they can avoid all this.
They ought to oppose them for that very reason. It’s one thing for a person to be committed against their will, which requires due process, and them be deprived of rights. It’s another to say because you one saw a therapist for depression or some other issue that you can no longer possess a firearm. The key is due process. I’m OK with people being deprived of rights through due process, but not administratively. Once a bureaucrat gets to decide, then it’s not a right anymore.