To lose 2 pounds a week, you'd have to stay around the 1,500 calorie mark. I'd say that the kinds of foods you eat are more important than the amount though. Make sure they're whole, satisfying foods that are low on the glycemic index. Drink all your water, make sure you get in some healthy oil each day (2 t. is the recommended amount), and at least two servings of dairy.
You can lose weight on Core but in my opinion, it's a difficult thing because they leave the limits up to the individual. "Eating til satisfied" is different for everyone, and most overweight people obviously don't know the signs of being full. I recommend that you still count your calories (or points) while eating from the Core list of foods and see how you do with it.
In order to see a loss, you have to create a calorie deficit which means taking in less than you use. It's the only healthy way to do it. The myth of "you're not eating enough" is baloney, in my opinion.
My two cents' worth.