And you are incorrect. Some 25 - 50% of sales at gun shows are made by non-FFL sellers -- no background checks required in many states. That's a loophole big enough to drive a truck-full of terrorists or lunatics through.
If that's your issue then outlaw any private sales of firearms _ANYWHERE_ Eric or block advertising in the classified adds of newspapers & the 'net for private sales of firearms.
I, personally, wouldn't sell any of my weapons to anyone but a FFL dealer or someone who was known to me. But then that's just me.