Doesn't "Baghdad Jim" receive threats on a regular basis? What's new.
What would be more productive is to give some thought to dealing with the Mentally Impaired that are given some pills, told to take them, and then released to the street with little or no supervision. The warning bells were rung a long time ago with this "fruitcake" in Tucson but nobody, most importantly the parents, took any meaningful action.
We've had police officers killed by "mental cases", an attempt on a President (Regan) by someone with real mental issues, and other cases where some early intervention and identification could make a difference. Instead we wait, afraid to take any action until they kill someone, or a bunch of someones. At the very least, intervention only to the extent that they are identified as Mentally Incapable, they become "known to the system" and those who should not have firearms can be ID'd and sales prevented by Dealers.
Others will have differing views on that last point but in the Tucson example it might well have prevented him from obtaining a firearm.