His post is here. I would say that there is a decent probability that he is correct. However, below are some potential counter-arguments. I will also address Don Boudreaux.
On the point that past forecasts of technological unemployment have been wrong, I agree. If history is any guide, then eventually a new economy will emerge in which pretty much every worker is much more productive than before. On the other hand, Moore's Law might produce technological change that is much faster than what we have experienced in the past. For humans to keep up, we may need brain implants or other technological enhancements.
The point that low-skilled workers were doing better a few years ago is not totally compelling. They were productive in the context of an unsustainable housing boom. One way to read the last ten years is that the exceptional years were 2005 and 2006, not 2008 to the present. The basic trend is accelerating substitution of capital for labor, a process somewhat masked by the bubble.
The point that third-world workers are employed refutes the Z in "zero marginal product." I would agree that American workers could compete for jobs at third-world wages. But it still could be that marginal product is well below first-world wages.
Finally, Bryan suggests that because wages have not fallen, then the marginal product of workers need not have fallen very far. But if the marginal product of workers has not dropped, then it is hard to explain why so many jobs have been eliminated. Average productivity has been growing quite well, while average real wages have flat-lined. If this were true on the margin, then labor demand should have increased. Instead, as Tyler Cowen puts it (see the video of the year), it looks as though firms are raising average productivity by replacing/shedding workers. And shedding workers only raises average productivity if marginal product is significantly lower than average productivity.
Even the lowest-skilled worker is capable of producing something of value. And the value of using that low-skilled worker to produce that something, rather than using some other means (i.e., a higher-skilled worker or a machine) to produce that something, rises the greater is the comparative advantage of those other means at producing something else.
That's easy for an economist to say. In the real world, try to figure out what that something is. That is what I mean by finding PSST. If these patterns could be discovered instantly, then there would be no unemployment. However, in a complex world, it is difficult. As it gets more complex, it becomes more difficult (other factors, such as better communication technology, may work in the direction of making it less difficult). One hundred years ago, if you did not know what else to do, you could offer your labor to a farmer. Today, the farmer can not find anything that you can do that is worth a subsistence wage.
Imagine a construction project where the project manager has just discovered a major problem with the plans. The design needs to be reconfigured, and workers need to be redeployed. But until the project manager comes up with a new plan, the other workers are all ZMP. Think of the economy as being like that construction project, except that there is no project manager. There are only entrepreneurs acting in a decentralized fashion, guided by the price system. They don't get it all sorted out right away. Until they do, ZMP prevails.