1.  END THE DRUG WAR!  The drug war contributes to a great many of the gun deaths thru gang violence and such.  Beyond the direct contribution, it also indirectly contributes by tying up the courts and law enforcement with enforcing laws that contribute to their bottom line (civ forf) and to their egos (trotting out seized drugs, military equipment, and dogs).  Get the judicial system and the cops back to dealing with violent crimes that occur beyond the desire to smoke pot and take heroine.  Free up the resources to deal with tracking domestic abuse and other violent crimes.

2.  Allow the CDC to research and report on gun violence as it should be as a human cause of death.

3.  Suicides and other mental health issues contribute to much of the death.  Somehow find a constitutional way to bridge the gap between rights and allowing/encouraging/forcing people to give up firearms when in such a state.  Treating mental health as a health issue would be helpful.  This one is the hardest I think.

4.  End the loop holes for background checks.  All gun transactions should be checked (locally - sheriffs), background (national database) and mental health (very tough . . . I dunno).  All people obtaining a gun should have to take a training course and be certified.   We don't hand out weapons in the military without training them.  The more dangerous the weapon (capacity, distance, etc) the more onerous the certification and training.  Of course this means enforcing the existing laws . . . which we don't seem to be doing.

5.  Don't expect gun violence to disappear.  Expect any of these measures to be like enforcing seatbelts.

IMHO the only one of these things that could violate the constitution is the mental health thing . . . It was never intended that citizens would have access to guns without a duty involved.  That duty is at most to die in the service of your country . . . at least to be trained and certified for their use. 

...  How many supposedly intelligent people actually think they can WIN the drug war?  Do they really actually believe that?  It's absurd.