Right now, it's sitting in temporary storage facilities, many of them near major metropolitan areas, vulnerable to accidents, environmental disasters and terrorism.
Every possible solution has been explored, from dumping it in the ocean to launching it towards the sun. Finally, President Bush, the Department of Energy, and the U.S. Congress decided that all of that nuclear waste should be moved to Nevada and buried under a mountain in the middle of the desert.
Needless to say, people in Nevada aren't crazy about this idea, and, as Correspondent Steve Kroft reported last fall, they believe most Americans will agree when they find out how the plan might affect them.
Yucca Mountain sits on federal land in Nevada, not far from Death Valley, in a remote stretch of desert, 90 miles northwest of Las Vegas. The nearest commercial establishment is a brothel 15 miles away.
If the U.S. government has its way, this will be the final resting place for 70,000 tons of highly radioactive nuclear waste. Beginning in the year 2010, it will be shipped here from all over the country by truck or by rail, and stored under the mountain in tunnels for the next 10,000 years -- which is how long the waste will remain deadly.
Mike Voegele, the chief scientist at Yucca Mountain, gave 60 Minutes a tour.
Even in stainless steel casks lined with lead or depleted uranium to absorb the radiation, the nuclear waste will still be so hot and so dangerous it will have to be moved with remote-controlled machinery.
"The temperature might be in the range of 300 degrees Fahrenheit," says Voegele. "Very, very hot."
The nuclear waste is currently being kept in temporary facilities scattered across 39 states, in cooling ponds and in storage buildings outside nuclear reactors. Some of it sits adjacent to rivers or on top of water tables. Secretary of Energy Spencer Abraham says 161 million Americans live within 75 miles of one of these sites.
"We think that it just stands to reason that consolidating the waste in one facility in a very remote part of America will make it much easier to protect on a long-term basis," says Abraham.
How important is the Yucca Mountain Project to the United States?
Abraham says it's critical: "We need to find a permanent storage facility so that communities that have the waste building up can get rid of it. And without doing that, we'll have not only environmental challenges, but we, I think it will undermine our energy security and our national security."
With the president and Congress on board, billions of dollars already in the ground and only one more regulatory hurdle to clear, using Yucca Mountain to store nuclear waste might seem like a foregone conclusion. But the battle is far from over, and the state of Nevada is in full-scale revolt.
A coalition of elected officials, environmentalists and businessmen is waging a guerrilla war to kill a project they believe has been shoved down their throats.
One of them is Brian Greenspun, the president and editor of The Las Vegas Sun: "Congress started looking around and said, 'OK, let's bury it someplace.' 'OK, who has only two senators and only one representative, no political clout whatsoever? And who lives in a place that is perceived, at least, to be nothing but desert and wasteland?' And they said, 'Ah-ha! Nevada.'"
The federal government still owns 87 percent of the land in Nevada. But people here say all roads - not to mention rail lines - lead to Las Vegas. When the Yucca Mountain project was first proposed 20 years ago, Las Vegas was still a fairly small city.
Today, with a population of 1.6 million, it's the fastest growing metropolis in the country. Approximately 5,000 people move here every month, and there are 35 million tourists who come here every year.
City fathers say if you look at the existing transportation routes, as much as 85 percent of the nuclear waste could have to come right through the metropolitan area on its way to Yucca Mountain.
"Makes no sense to me. Who wants to be the unlucky person who's here outside a hotel on the Las Vegas Strip when one of those trucks turns over and the nuclear waste spills?" says Greenspun. "And you know it's going to happen. Accidents happen."
The mood in Nevada is one of outright defiance. The state is trying to kill the project by denying water to Yucca Mountain, on the grounds that it is not in the public interest. And Las Vegas has passed a law making it illegal to haul nuclear waste through the city.
Mayor Oscar Goodman says he plans to enforce it: "If it comes by rail, the only rail goes right through the heart of my city. And I guarantee you one thing: as long as I'm the mayor, it ain't comin' through."
How does he plan to stop it?
"If I have to put up barriers up and arrest whoever is trying to transport it, I promise you that's gonna be done," says Goodman. "I'm dead serious."
Mayor Goodman says this isn't just a case of Las Vegas or Nevada screaming "not in our backyard." The nuclear waste will have to travel through a lot of backyards before it gets to Nevada.
The Department of Energy (DOE) hasn't disclosed exactly how it plans to get all that nuclear waste to Yucca Mountain, except to say that it will be transported by rail and heavily guarded truck convoys over the interstate highway system, and require between one and six shipments every day for 24 years.
But Dr. Robert Halstead, who's been a transportation adviser to the state of Nevada since 1988, says if you take a map of the U.S. transportation system and mark the locations of nuclear facilities, you get a pretty good idea of potential shipping routes.
"They would heavily affect cities like Buffalo, Cleveland, Pittsburgh, in the Chicago metropolitan area, in Omaha," says Halstead. "Coming out of the south, the heaviest impacts would be in Atlanta, in Nashville, St. Louis, Kansas City, moving across through Salt Lake City, through downtown Las Vegas, up to Yucca Mountain. And the same cities would be affected by rail shipments as well."
Halstead said when Congress voted last year to go forward with the Yucca Mountain project, it did so based on poor or non-existent information about how the plans would affect their states or congressional districts.
Does Halstead think the DOE is intentionally holding back that information?
"Sure. I think it's part of DOE's political strategy to withhold information about the transportation impacts from the Congress. Period," says Halstead.
Nevada Sen. Harry Reid, the second highest-ranking Democrat in the U.S. Senate, agrees: "Stuff isn't gonna suddenly appear out of the sky and be in Yucca Mountain. You have to get it there some way. And that's the problem."
Reid says the devil in the Yucca Mountain project is in the details.
"How are you going to haul the most poisonous substance known to man across the highways and railways of this country? Thousands of miles through cities, towns, past farms, past businesses, churches, schools, residences," says Reid.
"This is the big secret that the DOE has. We'll give you that later, folks in America. In the meantime, we'll just say we have a repository in Nevada."
If most of the nuclear waste moves by rail (a plan now favored by the Department of Energy), the city most affected would be Chicago, where shipments from the East Coast would have to be consolidated, then re-routed to Yucca Mountain.
"One out of every three rail shipments would go through the metropolitan Chicago area," says Halstead. "One out of every six rail shipments would actually go through downtown Chicago within a mile or so of Lake Michigan and the Art Institute."
Secretary of Energy Spencer Abraham didn't deny it.
"I think there's a general understanding that we move hazardous material in this country. I think there's an understanding that the federal government knows how to do it safely," says Abraham.
"No routes have been finalized. We haven't made decisions yet. We are gonna do it safely. We're gonna do it in concert with local communities and state governments."
And Abraham says the government has been transporting nuclear waste for the past 30 years, but most of the shipments have been relatively small and not clear across the country. While there have been a few minor accidents, none of them have resulted in significant releases of nuclear materials.
"I would stress that, that we move much hazardous material via rail and via truck in this country today. And we know how to do it in a fashion that is safe for the public," says Abraham. "We are, we are not going to endanger the public."
The casks used to transport nuclear waste have been smashed into concrete barriers, broadsided by roaring trains, dropped from high altitudes and burned in jet fuel for 90 minutes. They've stayed intact, but how secure are these casks? How durable are they?
"They're among the best containers that humans know how to make to contain hazardous materials," says Halstead. "On the other hand, the payload is so hazardous that only a tiny fraction has to escape in an accident or in a terrorist incident in order to have a disastrous or even a catastrophic clean-up cost."
Halstead says the casks are not designed to withstand all disasters, like the Baltimore Tunnel fire in July of 2001, when a freight train carrying hazardous materials derailed and burned for four days with temperatures inside the tunnel reaching 1,000 degrees.
But it's not just accidents Sen. Reid fears. He worries about terrorism.
"Every one of these trucks, every one of these trains, is a target of opportunity for a terrorist to do bad things," says Reid. "I mean, you talk about a dirty bomb. I mean this is, this is really a filthy bomb."
Twenty years of tests and studies have demonstrated the vulnerability of the shipping casks to a variety of possible terrorist weapons, concluding they can be breached by explosive charges or anti-tank weapons.
"These caravans so far are going to be 300 feet long -- a football field long," says Greenspun. "Going 35, 40 miles an hour across the federal highways. Do you think it's going to be hard to hit that with anything? Even I could hit it."
Could they be blown open by a demolition charge? Could they be blown open by a shoulder-fired rocket?
"Well, the question I think you should be asking is not whether those casks can be attacked only, but whether or not the current location of the nuclear waste is a more vulnerable target," says Abraham. "We have invested $4 billion in the science and the safety. And based on that investment, I am confident that we know how to do this in a way that's safe. Yes, it can be trusted."
But trust is a rare commodity in Nevada when it comes to the federal government. Many people, like Greenspun, still think of themselves as nuclear guinea pigs. He remembers watching atomic bomb tests with his father back in the 1950s.
"He would take us up to the top of Mount Charleston when we were little kids, so that we could watch the blasts. You could see the mushroom cloud go off. And we thought that was the neatest thing in the whole world," recalls Greenspun.
"And then, minutes later, this pink cloud would come over and we would get sprinkled with dust. No one ever thought anything of it. Thirty-forty years later, we are the thyroid cancer capital of the world."
This is a fact that has not escaped the notice of Mayor Goodman, who keeps a copy of a 1957 handbook on those nuclear tests put out by the Atomic Energy Commission.
"They say that fallout of this contaminant, this radiation, this deadly material, can be inconvenient. That's the way they expressed it," says Goodman. "So I'm not going to help the federal government lie to us again. Nope, not, not during my administration."
The state of Nevada is still battling to keep Yucca Mountain from opening. It sued the federal government to stop the project, and it's trying to stall the Department of Energy's efforts to get a license to operate the site.
Nevada also has recruited a powerful ally in its fight. Democratic presidential candidate John Kerry told Las Vegas voters that he's against the project. There will be no Yucca Mountain nuclear waste depository in a Kerry administration.