Hubbert accurately predicted when the US would reach it's peak rate of oil production and depending on which end of the spectrum you look at, the global rate of oil production has already peaked or will in the next 10-15 years. meanwhile, worldwide demand is continuing to increase. Oilfield discoveries peaked in 1965. Over the past few years it has become clear that proven oil reserves have been greatly overstated by as much as 20-50% (some of this by oil companies own admissions). Meanwhile, global demand (in bbl/day) is continuing to increase, putting upward pressure on prices.
Sure, there is a lot of oil left in the ground from any field, and to get that out will cost more and more money. This will put increased price pressure on oil derivatives and thus impact the global economy, particularly the cost of food production (see Hirsch report from the US Dept of Energy).
If you had continued to read the book, you would understand that it isn't simply about how much oil is available, but also how intertwined oil is with our government and economy, and how difficult it is for us to move to alternative energy in order to offset the impact of oil price shocks. This is the same thing that happened to the Dutch who couldn't transition from wind power to coal in the 17th Century. They were surpassed by the English Empire who's economy was based on a new, more efficient, energy source called coal. Likewise, our empire was built on oil (yes, the US uses a lot of coal but we exploited oil's high efficiency and portability) and it didn't take long for us to displace the UK as the world's dominant economic power. Great Britain could not transform it's coal-based economy fast enough to keep up with the US. What Phillips warns us about is the scelerotic nature of our oil-based economy and political structure that cannot transform itself fast enough to compete with the shiny new industries of China, which are powered by high-efficiency alternative energy, natural gas, and petroleum.