The world cannot run on electricity alone, without a very major transition from where we are today. At a minimum, this would take 50 years, if it could be done at all.
One of the issues we have is that decommissioning of old reactors cannot be done without oil, at least the way the world is put together today. Also, the world is likely to become a poorer and poorer place financially, going forward, without the benefit of cheap oil. That by itself will make it very difficult do do anything with old nuclear plants, and with spent fuel rods. People claim that there is a possibility of the spent fuel rods at Fukushima colliding and causing a huge reaction, if, for example, there is an accident in decommissioning, or if there is an earthquake that shakes the area further. I don't know if this is true.
So even if we have uranium, this doesn't get us around the oil problem, unless we can convert all of our devices to run on electricity, or we can make a cheap liquid fuel to run them. Cheap is an important part of this issue. An expensive fuel doesn't get us very far, except fianancial collapse.