As SMX said, the fundamental law of the United States guarantees the "the right of the PEOPLE to bear arms".
It is part of American culture, and illegalizing guns would just create a black market underworld in them which would give rise to something comparable to the mobsters during Prohibition in the 1920s.
Moreover, someone who is going to commit a pre-meditated crime such as a school shooting (and psychologists have found that they're often planned months in advance) can easily obtain any gun they want on the black market. This means that illegalizing guns would just punish responsible citizens who have committed no crime.
The previous government in Canada tried to establish a "registry" for long guns (hand guns have been illegal here for over 80 years, unless you're a peace officer). The original projected cost was about $100,000,000, but it quickly skyrocketed to over ONE BILLION DOLLARS. The system basically treats citizens as criminals just for having a gun - it requires them to pay huge fees and have their privacy invaded on a regular basis. The registry is run by urbanite bureacrats from Southern Ontario who only see the negative side of guns in city life. They don't know about responsible gun owners in the "hinterland" of the country, where people use them on farms, for hunting, or for marksmanship hobbies.
Here's how ridiculous the Canadian system really is: I am a member of the Canadian Forces Reserve (like the National Guard in the USA), I have a liscence from the Federal government to run small-bore target ranges (basically .22 calibre rifles), and I have never been convicted of a criminal offense - not so much as a traffic ticket. BUT because of this law, I am not allowed to officially own the rifles my grandfather gave to me on his deathbed.
So, gun control does not work to stop crimes or rampages. It punishes private citizens and leads to incrased government waste. Education about responsible gun use is what will stop these things.
Finally, was anyone aware that same day of these shootings in Virginia that over 70 people were killed in a bombing in Iraq? Why are American lives more newsworthy than Iraqi ones?