These weapons are designed for war- to slaughter multiple people at a time. Why would one need that in one's daily life for self defense? The majority of armed attacks are initiated by 1-3 people, not large mobs of armed men. The law would still be in tact. The goal is to make America as safe as possible, and the idea is to avoid losing as many innocents as possible. This law will enforce that.
The right to bare arms is still intact when citizens aren't allowed to carry what would be classified as assault weapons.
Virtually all handguns would remain legal to possess, as well as 2,200 hunting and sporting rifles. If that isn't enough, then I don't know what is.