Even if this is possible, it doesn't mean it is probable.
The authors of the book The New Atkins For a New You have said in an interview that this kind of weight loss is not the norm, and when it does happen, it is usually to people who would be classified as obese. And even for some of those folks, it does not always happen that fast.
And even if it happens, that doesn't mean you continue to lose at that rate after the two weeks. Let's say you lose 7.5 pounds of water one week, then lose, let's say, 6 pounds of water the next week along with 1.5 pounds of fat. Does this pattern remain constant throughout the coming weeks?
No. You are "out of" water weight to lose, and will then start losing fat at the rate of 1/2 pound to 2 pounds per week, depending on many factors, including, but not limited to, the amount you have to lose altogether, your age, your dieting history, medications you are taking, and so on. In some cases, you may not even lose 1/2 pound per week.
So not only will your weight loss slow down, most likely, but the closer you get to your goal, the slower it will probably get. If you have 40 pounds to lose, it could realistically look like this, even if you lose quickly at first, which many people don't:
Week 1 - 7.5 pounds
Week 2 - 7.5 pounds
Week 3 - 1 pound
Week 4 - 1.2 pounds
Week 5 - 0 pounds
Week 6 - 1.5 pounds
Week 7 - 0 pounds
Week 8 - 1 pound
Week 9 - 1 pound
Week 10 - 1 pound
After 10 weeks, it would not be surprising to go a couple or a few weeks without losing anything, and then drop 2 or 3 pounds suddenly, then go back to losing a 1/2 pound or 1 pound per week for the next couple of weeks, and then stay even again for a while.
The closer you get, the more likely that you will slow down, maybe even painfully slow down!
To think that because Atkins says it is possible to lose 15 pounds in 2 weeks, does not, therefore, mean that it is normal to continue that trend and expect to lose 2.5 or 3 pounds every week, consistently, for the next 14 weeks.
Here is the actual meaning of the quote - "You can lose up to 15 pounds in 2 weeks" means that you can lose between 0.000001 pounds and 15 pounds in two weeks.
If you lose 0.000001 pounds in two weeks, the statement is still accurate.
Saying you can lose UP TO 15 pounds, is not the same as saying you WILL lose 15 pounds.
The following statement is also true:
You can lose UP TO 1,000 pounds in 2 weeks. See what I mean?
So the moral of your story with Atkins is that your body will let go of the fat when it is good and ready. You may be doing every perfectly and still not lose very fast.
Think of it this way - Atkins is a way to get healthy, and as you get healthy, your weight will adjust to a normal healthy weight, whether it happens fast or slow. Either way, you win!