Recent publications from countries in which guns have been completely banned have proved that the ban does, in fact, reduce crime. This argument, of course, is completely separate from the idea that we need to arm ourselves in case the government becomes too oppressive. In the case of crime, it has been shown over and over again that fewer guns equals fewer crimes.
There are many illegal ways to get a gun in any country, whether certain types of guns are banned or guns completely. I'm sure someone has brought an automatic firearm into California before. Plus criminals would report to stabbing or otherwise to kill their victims. And also, I don't think the law is a good one in terms of effectiveness; so far I haven't seen one part of the law that takes guns away from criminals-only law abiding citizens. Put better background checks or something, this is ridiculous!
Crime will not be reduced because people will find ways to illegally obtain them. Many crimes are not committed by people that actually own the firearm because there are measures to prevent certain people from purchasing and owning a gun by requiring all firearm dealers to run a check through the FBI before selling a gun. Furthermore, this issue goes much further than it being a Constitutional right to bear arms. The people that rely on hunting as their food and/or income source and individuals that have a gun for safety reasons would be at a great disadvantage if guns were banned.
A ban on guns would not reduce crime, the same way a ban on abortions will not reduce abortions. What it does reduce is safety. People will go further and do much worse things to acquire firearms. They will begin manufacturing them and purchasing them from other countries, and fights for access t firearms may cause more violence. There are also still many other types of weapons accessible to criminals that will be used just as much if not more say they banned guns. Crime is not reduced, it is exacerbated.
Assume that somehow, you've enforced a perfect ban on guns. All you've done is made sure that the majority of people don't have them- therefore, they're removed from the equation. Guns are replaced with knives, and crime continues, except with more stabbing and less shooting. Studies have been done on the difference between states with gun laws and those without, and there is no noticeable difference crime.