how many days would you have to eat at a severe calorie deficit before the body would enter into the much talked about "starvation mode"?

i am curious because there are days when i have a really hard time hitting my calorie goals and i dont want to screw up my diet this way.

The answer is "It depends". It depends on how many low calorie diets you've been on. IIt depends on how often you go into a deficit. It depends on how active you are. Generally 2-3 weeks can create a stall.