Not to seem like a luddite, but let me play the devil's advocate here. 15 years, IMHO, a huge exaggeration. The standard technology of today: IVRS systems suck so bad that they make me want to slam the phone down after 2 minutes, if I cant talk to a human. Siri or GoogleNow aren't much better. When you force a human to interact with a computer, you are handicapping them and taking away most of their expressiveness. Guess what, humans don't like that. You reduce them to the level of the computer which can only understand a few pre-programmed options. That seems like a far cry from human communication which it will try to replace. And we don't even know if that's possible even in principle. All we have is the hope from a bunch of people who are generally excited by technology, and the ensuing hype.
Keeping Amara's law in mind, I would imagine that such a drastic change would take a longer time (almost 1 generation's working life?). Incremental changes summed up might displace jobs over decades, but if someone can adapt to those incremental changes, I would imagine that they can manage their whole working lives. At least as applicable to people born till (say) 2000 and would presumably live till 2100 or so. Any "predition" beyond that would be a wild leap. As for humans being born circa now...
However, I believe that a few questions are still of supreme importance and we need to tackle them for the sustenance of mankind (pun unintended).
1. If a computer/robot could exactly replicate a job (and do it on a macroscopic scale), will such a solution be energy efficient? [Assume that you already have a population of X billion whose needs you will have to meet]
2. What is the real aim of automation? Is it to save costs from the perspective of the business owner, or to give people leisure?
3. Let's say robots/computers replace a large segment of jobs. Presumably, a small number of people will own and operate those systems of scale (you just have to make a 3D printer which can print other 3D printers). Then what is the role of the "unemployed" humans? And most importantly, any such structure we come up with, must lead to a stable society.