If you mean pure protein yes that will kill you (look up rabbit starvation.) You might get by without carbs for a good while but all protein and no fat would be deadly, at least 0.3g/day of fat per pound of body weight is considered to be the healthy bare minimum to keep your hormones from crashing.

I have heard of one morbidly obese guy who went on a multi-month fast but it was under constant doctor monitoring and needed a lot of multivitamins every day.