The NICS system is supposed to block people who have felonies or are otherwise barred from having a gun from getting one. But it doesn’t. Why not? Because it doesn’t have complete information. If someone is deranged, hearing voices, psychotic, etc..., they would have to have a criminal record already to be blocked. Do you want to block these individuals from buying a gun or not?
The right of the People to keep and bear arms shall not be infringed. The problem, as pointed out up-thread by others, is who is deciding which folks are not allowed to buy a gun. Put in a mental health provision and tea partiers, people posting on freerepublic.com and people opposed to Obamacare will be declared unstable and denied a God given right.
Short answer is no, we have a right, pre dating the Constitution, to keep and bear arms. Felons get guns on the black market, steal guns or use other tools if guns are not there. Cain killed Able with a rock.
Use a little logic. The places with lax gun laws, like Texas and Arizona, have less gun violence than Chicago, New York and DC where legal guns do not exist. But somehow in DC, where a spent .22LR case nets a $1000.00 fine and jail, there is lots of gun crime.
A Navy facility with metal detectors, armed guards and the strictest gun laws in the nation left all those people defenseless. Paper laws do not stop bullets.