Actually, since there are no refined foods and very few grains it is not difficult to stay within the calorie range. This diet relies heavily on meat, yes, but also on fish, vegetables and fruits. I am NOT a nutritionist, but it should not be a problem to stay within the calorie and nutrient ranges while on the paleo diet. It may be that you will need to focus more on leaner cuts of meat (grass pastured meats tend to be leaner anyway), fish, and veggies rather than the more calorie-dense foods.
Good luck on whatever foods you choose!