Not sure what they can really do, since there isnt a huge amount of actual AP ammo even out there, let alone I cant remember any used in a crime.
Originally Posted by POTUS Press Release
Finish the job of getting armor-piercing bullets off the streets: It is already illegal to manufacture and import armor-piercing ammunition except for military or law enforcement use. But it is generally still not illegal to possess or transfer this dangerous ammunition. Congress should finish the job of protecting law enforcement and the public by banning the possession of armorpiercing ammunition by, and its transfer to, anyone other than the military and law enforcement.
ETA: the only thing I can see POTUS pushing is a ban on possession of AP by his above statement...Unsure if they could go after common jacketed hunting ammo, but who knows.
Perhaps this may cause a look into the handguns chambered in rifle calibers as well...Again, to soon to guess.