It depends on what your eating Say if you eat only meat everyday and nothing else you wont be getting all the nutrition you need and will probably feel sick. As long as you are getting all the nutrition you need you wont get sick but yes eating the same thing every day can make you sick.
I tend to be a creature of habit when it comes to food but only for a few weeks at a time. These last few weeks were grilled chicken breast sandwiches and cans of pineapples. My body gets used to it and burns it better. I've lost 11 pounds so far simply by losing the soda and drinking lots of water! Your results may vary.
What you mean by sick? Vomitting? No it wouldn't make you sick. I used to eat scram eggs everyday when I was young for a long time. I ate it until I got tired of it,occasionally have them now,but variety of food is always healthier.