Okay this is from the World Nuclear Association, so take it as you will:
Supply doesn't seem to be a problem.
If we compare apples to apples, existing nuclear power supplies and equipment are not a very enticing alternative to existing renewable energy sources. Counting cradle-to-grave reactor costs they aren't that cheap, and counting only the uranium we know we can set our hands on, if the world built ten times as many reactors as we now have the world would run out of uranium very quickly.
The Australian government had a committee look at them some years ago and the conclusion was that even though our uranium reserves are significant they aren't a long-term energy solution, and we are at least as blessed in terms of potential renewable energy sources as we are blessed in terms of fissionable molecules in our ores. So why go with the short-term nuclear solution with all its attendant problems, when we could put up solar panels, or wind farms, or wave power stations, or whatever? We could still be getting energy out of solar in three hundred years time, and we wouldn't be passing on a burden of nuclear waste to future generations to do it.
That's not mentioning the weapons proliferation issue.
Don't even mention fast breeders - they're disasters waiting to happen and they only exist because they're good for making weapons-grade material. They are not magical genies that transform nuclear waste into daffodils, or if they are nobody has demonstrated that it's a cost-effective energy solution.
Also comparing apples to apples, pie-in-the-sky nuclear reactor technology could solve all our problems at once and bring about Utopia, and pulling uranium out of sea water and whatnot is still at the pie-in-the-sky stage. Nobody's demonstrated that they can do it on a large scale cost-effectively. It's all "we did a pilot project, and if we conveniently assume large economies of scale, and don't show all our numbers, it looks wonderful!".
If we're allowed to appeal to science fiction, which is what the nuclear lobby's pie in the sky amounts to, renewable science fiction technologies could also save the world and bring about a glorious new age of energy too cheap to meter and all that.