Let's dispense with the rhetoric for a moment, and look at some numbers.
I came across the following on Wikipedia while looking for something else. It's from a data set produced by the Bureau of Justice Statistics breaking down homicides in the US by the weapon of choice. Here's the graph that appears on Wikipedia:
However, I do think it is fair to argue that the marginal homicide in the US is--statistically speaking--committed with a handgun, because again: note that the rates of homicides by other means are really, really stable year over year. Put another way, the difference between a homicide and a non-homicide may very well be in many cases, having a handgun with which to commit it, or not.
Whatever your predisposition is regarding guns, public funding for mental health services, criminal justice policy, or any of the other arenas of debate that impinge on the question of gun violence in America, I should hope it is safe to assume that everyone is interested in having fewer people die violent deaths. The points of contention, really, aren't about the ultimate goal, but rather 1) how best to achieve that goal, and perhaps 2) how one weighs the trade-offs involved in policies pursuant to achieving that goal.
Too often--and especially after high-profile mass shootings--the argument is made that "nothing could have prevented this." This is problematic, not because it is untrue in many of those particular cases, but because it tends to lead to the--perhaps unconscious--conclusion that all homicides are therefore not preventable. Clearly, no one seriously believes this; if every homicide (or indeed any crime) is an utter inevitability, why bother having a criminal justice system at all? And yet it seems an article of faith among many in this country that all efforts to reign in our culture of gun violence via tighter regulation of guns are ultimately futile.
That said...it is entirely fair for gun rights advocates (or anyone) to demand a measurable positive return on a change in policy, particularly a policy that abridges (or that they consider to abridge) their own personal freedom (see point #2 about trade-offs above). And if the metric we are using to evaluate that positive return (or lack thereof) is the total homicide rate, I'm not sure that it makes sense to fret too much about assault weapons or large magazines.
If we're serious about reducing total homicides via reducing the number and/or types of weapons in general circulation, it makes a great deal more sense to go after handguns. Given the number of people that own handguns in this country, that is naturally a much more difficult proposition.