Josh Sugarmann, who seems to be the brain trust for the gun grabbers, had already worked up a campaign against civilian semi-auto assault rifles, based on their "scary" looks and deliberate conflation of them and real military selective fire assault rifles ("machine guns", although often it's just a 3 round burst for better control). And then the Stockton schoolyard massacre happened (http://en.wikipedia.org/wiki/Cleveland_School_massacre) and off they went.
(A couple of notes on things you won't get from that article: Purdy was able to legally buy his weapons with his SSI money because his crimes had always been plead down to misdemeanors; I'm also pretty sure he never passed the 18 U.S.C. 922(g)(4) criteria for a mental disbarment, so even if the NICS had existed then it wouldn't have stopped him.
Great emphasis is placed on these weapons being "high powered" ... which by definition they are not. And being based on military designs the cheapest ammo is FMJ, which is also the least wounding (Hague Convention requirement to make war more "humane"). According to Martin Fackler this resulted in ER doctors excessively debreiding wounds from them, resulting in greater morbidity and mortality under the real word got out.
I mention that because a lot of these efforts have very nasty unintended consequences, e.g. the whole "cop killer bullet" campaign about bullets that were never for sale to civilians did result in one thing: teaching a lot of criminals that a lot of cops wear concealable body armor....)
Anyway, you're right: if you really want to save lives, and/or want to minimize damage to your political side/party/whatever, it's a terrible approach. Cost the Democrats the Congress in 1994, according to no less a political genius than Bill Clinton.
Why does it keep coming back? I suppose it's viewed as low hanging fruit, easy to propagandize, and while you may "generally support gun control", a lot of gun grabbers are quite explicit about wanting to ban all guns and will take anything they can get (note, for example, how few of the current proposals would even in theory have changed the Newtown, Connecticut outcome; I mean, the police took at least 14 minutes to arrive after the first 911 call). So, again, a target of opportunity; rational policy by anyone's lights is simply not relevant.