Hackers On Atkins
I know it's been pointed out in numerous other hosts, but the body really can survive long-term on less than 2000 calories a day, and in the short-term can certainly burn far less than 2000 calories a day. Part of it is genetic, and part of it is environmental.
Some people natually have a low basal metabolic rate, meaning that if they sat on their ass all day, occassionally shifting positions to avoid bedsores or to go to the bathroom, they'd probably burn 1000-1500 calories a day, regardless of caloric intake. These people get fat very easily.
Now even your "average" person with a basal metabolic rate sufficient to burn 2000 calories while sitting on their ass can induce a lower BMR by starving themselves. The body goes into a protective mode, and lowers the BMR. In addition, the body, either through hormones or low blood sugar/fat levels, induces a state of laziness whereby the person moves sluggishly, conserving a maximum of energy.
If you can't get your head around this concept, try the following experiment. Drink just 16-24 ounces of water, once a day, and eat foods low in water content. Your body will quickly (couple days, tops) adapt to this water "starvation" diet, and you will both sweat and urinate less often. You may be able to go a day or two at a time without peeing, though it well start to smell.
Also, watch your weight. You should begin to gain a few pounds. You're taking in less weight of water, and you're gaining weight. That's because your body is storing the water.
Now, once your body gets to its maximum waterlogged weight, start drinking like mad. Not all at once, either. Drink 8-16 ounces of water, 8-16 times a day. Aim for about a gallon of water (twice the recommended 8 8-oz glasses a day).
In the first day or two, you'll probably lose about 3-4 pounds. How can that be? 3-4 pounds of fat is 10,000-15,000 calories. You couldn't burn that much in a marathon! 3-4 pounds of carbs or protein is still a good 5,000-7,000 calories. Assuming you're still eating 2,000-3,000 calories a day like normal, you'd have to burn 7,000-10,000 calories. So how'd you lose 3-4 pounds in a day or two, when you were eating your normal food intake and drinking several pounds of water? You just pissed and sweated it all away. You pissed and sweated half a gallon more water than you were drinking!
You body can store and conserve that which is scarce, and gets rid of what it doesn't need when it's plentiful (the extra water stretches tissue and adds weight, so in general it's not a good idea to store a lot of it if it's plentiful. Luckily, this isn't a conscious decision, mother nature figured this one out millions of years ago).
If your body can learn how to run on less than half of the water it normally uses, how far of a stretch is it to think that it can conserve calories, even to the point of using fewer calories than your already low-calorie diet is providing?
Now don't get me wrong. There is a limit. For some people, because of genetics, they can't get below 1800 or 1500 calories, even when eating only 600-1000 cals a day. IANANutritionist, so I don't know the exact number, but I suspect the average person, if not overly active (i.e. you're not a construction worker, you're a desk clerk) could get their calorie burning rate down to in the 1000-1400 range. Meaning some would lose weight on 1200 cals/day, and some could gain (though certainly not more than a pound every couple weeks; the rest would be water weight, because you're probably making the mistake of drinking less while eating less. Drink more, and the water weight comes off as well).
And as has been mentioned, the body is highly adaptable. Meaning that, assuming you're taking multi-vitamins and getting enough fiber, amino acids, and omega 3's and 6's, you're body would adjust to the low-calorie diet, and would no longer consider it starvation level. Then your body would stop trying to store fat, and your BMR would rise again (though not as high as before the low-cal diet), and you would start to lose weight. But it would probably take a few weeks.