Your liver will happily produce all of the glucose your nervous system needs.
On the plus side, you'll be really sensitive to insulin when you do get some carbs into your system again :) And hey, I just read an article that said lowering insulin levels is the key to the longevity gains resulting from caloric restriction.
Reducing your caloric intake won't kill you and it has been shown in rats that it might even be good for you. Your liver only stores glucose, it doesn't create it (That would violate conservation of energy!).
This thread is talking about artifically spiking your blood suger which will rape your pancreas and eventually lead to diabetes. I wouldn't do it if I were you, but I might consider eating more vegetables and low calorie foods :-)