The Gun Deaths Keep Mounting Up

On December 14th of last year, 26 people were gunned down at the Sandy Hook Elementary School in Newtown, Connecticut -- twenty children and six teachers. It was a horrific occurrence, and has spurred new debate on gun restrictions in this country. But as terrible as it was, it is only a tiny fraction of the gun violence problem in the United States.
Since the Sandy Hook tragedy, another 3,300 people have died from gun violence in this country. That's in a period of about about four months, and it means that:
About 825 people per month have been killed
About 206 people per week have been killed
About 28 people per day have been killed
Whether the NRA and other right-wingers want to admit it or not, this is a serious problem. And it is a problem that no other developed nation has. It is caused by the proliferation of guns in this society, and the ease with which anyone, even criminals and the dangerously mentally ill, can get the gun of their choice (including rapid-fire large-magazine assault weapons which can kill large numbers of people in a very short time).
Can't we at least try to do something about these gun deaths? Can't we at least try to keep guns out of the hands of dangerous people? No one believes asking all gun buyers to pass a background check will eliminate all gun deaths, but wouldn't it be a reasonable and constitutional action that could lower the number of gun deaths? How can anyone justify doing nothing?