Is it possible to eat too few calories to loose weight?

I understand a fair bit about nutrition and how, basically, you have to be at a deficit calorie wise to burn fat. But how many calories is too little? I know the recommendation is to never go under 1200. My TDEE is 2168, and for fat loss the IIFYM Marco Calculator (the one in the FAQ?) I'm looking at the suggested "reckless" reduction of 25%, down to 1626 a day. If I'm reading this correctly, this is includes exercise? MyFitnessPal does things differently, and their suggestion to loose 2lbs a week was to go at 1200 cal, before exercise. Not to split hairs, but 400 feels like a big difference to me?