Just a quick note on your last paragraph, because that reminded me of the other data I looked at. I don't have the exact data handy (I'm doing some before bed hacker news browsing on my tablet), but I think it was assembled by, I want to say, a site called Mother Jones..? It was a google spread sheet of some kind. Anyway, it was a table with every mass shooting in the history of the US, the number of fatalities, and the weapon types used.
After I finished playing with the FBI's data, I started to wonder if the ban was not to stop the kind of day-to-day gun crime, but to prevent the mass shooting, High profile, high fatality events like the recent school shooting, or the Aurora movie theater shooting, or any similar event.
So, I pulled the data from that collection, and could find absolutely no correlation between rifle involvement in a mass shooting and the number of fatalities. Our worst shooting, with (going from memory here) 33 fatalities was the Virginia tech masacre. It involved absolutely no rifles, or shotguns, just the lowly handgun. I'll have to double check all the numbers tomorrow, but if I believe that in the 10 most dealy mass shootings in our history, of the 22 or so weapons used, only 4 or 5 of the were rifles. To my number crunching, rifle usage was pretty inconsequential in the number of fatalities -- which I'll admit was pretty damn unintuitive. But that's what the data shows, so given all that information, it's tough for me to figure out a reason for the administration pushing for the ban.