If you eat as much protein as you want, you’ll probably eat well over 1000 calories a day – so you probably won’t lose weight fast enough, to stay motivated enough, to stay on a low carb diet. If you eat less than 1000 calories a day of a full carbohydrate diet, you probably won’t lose weight at all, because you’ll be way too hungry, and you’ll have way too many sweet and starch cravings – to stay on less than 1000 full carbohydrate calories a day.