Scientifically, what to do with nuclear waste is a SOLVED problem. We know what to do with nuclear waste so that it isn't around for a long time and is disposed of safely; we reprocess / recycle the spent fuel.
Here's a description of the process from nuclear physicist Dr. Charles Till, who was Associate Director of Argonne National Lab when the following PBS interview was conducted about 15 years ago:
http://www.pbs.org/wgbh/pages/frontline/shows/reaction/interviews/till.html
Q: The fission products.
A: Fission products. But none of the long-lived toxic elements like plutonium and americium or curium, the so-called manmade elements. They're the long-lived toxic ones. And they're recycled back into the reactor ... and work every bit as well as plutonium.
Q: So they go in, and then those are broken into fission products, or some of it is. Right?
A: Yes.
Q: And you repeat the process.
A: Eventually, what happens is that you wind up with only fission products, that the waste is only fission products that have, most have lives of hours, days, months, some a few tens of years. There are a few very long-lived ones that are not very radioactive.
This is what other countries that use nuclear power, eg. France, Sweden.. do. They reprocess the fuel so that they don't have to look for a thousand year repository; the lifetimes of the waste is severely curtailed to the values given by Dr. Till above. There's no reason that nuclear waste has to have lifetimes in thousands of years. That was foisted on the nuclear industry by the 1978 Congress acting at the behest of the anti-nukes.
However, it looks like the USA is going to get its repository anyway:
http://thehill.com/blogs/e2-wire/e2-wire/316797-obama-administration-must-rule-on-yucca-federal-court-says
Court: Obama broke law with nuke delay
A federal court on Tuesday ruled that the Obama administration broke the law by delaying a decision on using the Yucca Mountain site in Nevada as a permanent nuclear waste dump.
In a 2-1 decision, the U.S. Court of Appeals for the District of Columbia Circuit said the Nuclear Regulatory Commission (NRC) violated a 1982 federal law by halting its consideration of the project. It ordered the NRC to deny or approve the Energy Departments application to store nuclear waste at the site.
PamW