I included the word "sufficient" as an ass-covering move, because one facet of the problem is we don't really know what will serve as a "sufficient" amount of training data in what context.
But, what specific types of tasks do you think machines still can't do, given sufficient training data? If your answer is something like "physics research," I would rejoinder that if you could generate training data for that job, a machine could do it.
I don't see how we anything like know that deep NNs with ‘sufficient training data’ would be sufficient for all problems. We've seen them be sufficient for many different problems and can expect them to be sufficient for many more, but all?
DeepMind's go AI, called AlphaGo, has beaten the European champion with a score of 5-0. A match against top ranked human, Lee Se-dol, is scheduled for March.