If we built fast reactors, we would have enough fuel, in the form of depleted uranium sitting around idle in barrels at enrichment plants, to supply the entire planet's energy for about 1000 years.
Current reactor designs, given current geologically-proven reserves and what has already been refined and available in world markets, is about 200 years. The definition of proveable is that someone's already done it.
Fast reactors aren't economical right now. Maybe in two hundred years, assuming no new sources of uranium are discovered, we'll need to revisit it. It's economically absurd right now to suggest switching over. The 200 years estimate is based on today's technology, with today's known quantity, in today's economy. Yes, there are technologies, like fast reactors, that can re-use the spent fuel -- but until we're out of enriched uranium, there's simply no need to.
This is a question for our great great grand children to answer, not us. We should be more focused on getting off fossil fuels before our problems are less about an energy crisis than about having a habitable planet to live on. We'll have fuel for nuclear reactors for as long as the planet remains habitable. Habitability is in doubt because we're more concerned with short term gain than long-term stability. I don't want our children to have to wonder where their next meal will come from -- you can eat the trees, grass, birds, wild life, plants... but you can't eat money.