His basic point is: We may not have hit peak oil yet, but production has maxed out. The major oil-influenced economic shocks come not from high prices, but from sudden price spikes. Since there is little to no excess capacity left in the world, the market is more susceptible to price shocks than ever before. Even small shocks can trigger disproportionate effects due to the lack of wiggle-room that was previously provided by Saudi Arabia's enormous (now nearly maxed out) production capability.
As he points out, no one knows for sure if the peak is already here or if it will take until 2035 or later to arrive. However, increasing volatility is inevitable and given the large role oil plays in the global economy, we can expect nasty surprises. Unless we plan for it. As Kevin points out, the economies can survive high oil prices, and they may even spur innovations to develop more elastic alternatives to oil. Market forces are able to take care of this, but we must begin taking it seriously and begin planning for higher prices.
Some thought also needs to be given to India and China's rapidly growing demand. It will quickly surpass U.S. demand and keep climbing.