First of all, I am not a doctor or nutritionist, but am just sharing what I know
I've heard of very low calorie diets (i.e., under 1000 cal), but have read that these types of diets are ONLY to be done under the supervision of a Dr. so your nutritinal intake and health can be monitored by a professional, as it can be dangerous or even deadly if done improperly. Usually a diet that extreme will only be advised for people who must lose a lot of weight very quickly in order to have a life saving surgery or something like that. So practically speaking, no, you shouldn't go under 1200 calories. (of course one day here or there isn't the end of the world...but women should have at least 1200 on average.)
Another thing to remember is setting reasonable goals. It's not unreasonable for someone 100 lbs heavier than you to want to lose 3 lbs a week, since a 257 lb person needs many more calories to "survive" than you do. 1500 cals for them might enable them to lose 3 lbs a week, but maybe only 1.5 lbs a week for you since your body is lighter and needs fewer calories to "survive."
Hopefully that kind of makes sense?