One or two stabs won't do it unless they are very well placed: The attacker will probably have to stab the victim repetedly, risking bodily harm, and getting a ton of evidence all over himself.
It's also easier to flee from someone with a knife than with someone with a gun.
It's also less common to accidentally kill someone with a knife. Accidental gun deaths happen all the time.
In the end, an assailant armed with a knife has less chances of succeeding, and even if he succeeeds, of getting away with it. It's not the gun's fault, it's just so much more efficient that it allows some people to act on urges they'd never go with using a knife.
Think about this comic book weapon: The Death Note. A book that kills any person whose name is written on it. The person seems to die of a heart attack. Almost impossible to trace a crime to the perpetrator, 100% success rate. It's hard to prove it was even a murder. Would the number of murders increase if people had access to such a weapon? Killing without risk or consequences other than guilt? Of course it would increase! Wife cheats on you? kill the bastard! Disagree with a politician? He's gone, and nobody can find you! It'd change the world as we know it. A gun is not quite as convenient, but in the same way, it makes crime happen that wouldn't happen otherwise.
Really? I'm pretty sure that anyone, who would actually kill another person, is not going to stop and say "Hey I really want to kill this person, but all I have is this knife. Oh well, guess I won't because it's not efficient enough."
There are a lot of problems in the USA, but guns really aren't one of them. There are major cultural issues causing the problems and people simply want a scapegoat for them. The nature of guns just make them an easy target.