The problem with Michaels' argument is the same problem that destroyed the Malthusian hypothesis. It fails entirely to account for how we change according to circumstances. Victorians used to worry that it would not be possible to dig enough canals to transport their wares, and that they'd run out of horse fodder. Hibbert worried in the twentieth century that we would run out of oil by the 1990s.
What actually happens is that technology improves. For each unit of GDP we now consume around 15% of the energy we used to consume to produce that unit seventy-five years ago. We no longer worry about running out of coal, or horse fodder.
As for food, we already grow 200% of what we need to feed 8 billion people; we simply waste half of it (poor logistics chains in the developing world, and over-consumption in the self-indulgent West). So by improving our consumption patterns we could arguably feed a population of at least 15 billion, though all estimates are that we'll see the peak at under 10 billion before global reductions down to around 6 billion within 200 years.
As we creep toward more renewable sources of energy, the unsustainability argument falls even flatter.
It's easy to draw straight-line extrapolations, but it's always the wrong thing to do. Life adapts and even stupid humans adapt eventually, thanks to the price mechanism that slowly drives us toward temporary equilibrium and spurs innovation and greater efficiencies.