And the roof over the swimming stadium? Greece recently gave up, and just decided not to build it.
The biggest construction challenge is the main Olympic stadium, where a giant glass and steel roof is supposed to go up.
It's envisioned as the architectural signature of the entire Athens Olympics. The organizers say, "Don't worry, it'll get done." But it is months behind schedule. Correspondent Lesley Stahl reports.
Ask Athens Mayor Dora Bakoyanni if her city is going to be ready by August, and she starts talking about Greek folk dancing.
"In Greece, we are like 'Sirtaki' dance. We start very slowly, and then we speed up. And then at the end, you cannot even follow how quickly it goes. So I believe that's exactly what happened with us," says Bakoyanni. "We might be afraid until the last minute, but I believe that we will be ready in time."
But the Greeks don't have nearly the resources of other countries that have hosted the Olympics. They're like the proverbial underdog.
"We're not the United States. We're not a nation of 250 million with all the logistics, infrastructure, and everything else you have," says Alex Rondos, who has helped shape Greece's plans for the Olympics – most recently as a top official in the foreign ministry.
"Greece is a country of 10 million people. Probably the smallest, the least rich country that has ever run the Olympics," says Rondos.
Of course, Greece has some things not even the biggest country can match.
In August 2004, the Olympic Games come home to the country of their birth.
Who else could stage the shot put at ancient Olympia, or run the marathon along its original route? But a grand history doesn't get stadiums built.
Bakoyanni admits that when Greece won the Olympics in 1997, they did nothing to get ready – for years. "That's unfortunately true," says Bakoyanni.
"Because we're a charming people who feel that they need to sit and discuss many things," says Rondos. "And I don't mean to be frivolous about it. We don't run ourselves like a bunch of drill sergeants."
Or, as someone else put it, bureaucracy was invented in Greece. If they'd tried to build the Parthenon in modern Athens, it might never have gotten done.
By the year 2000, things were so far behind schedule, the International Olympic Committee threatened to move the games to another country. The specter of national humiliation was enough, finally, to get preparations going in earnest.
"So, granted, there have been delays. And there's been inefficiency. Call it what you will," says Rondos. "The fact is that, as we approach the Olympics, not unlike the condemned man approaching the guillotine, it concentrates the mind wonderfully. And we are there right now."
Greece has done a lot. Stadiums for a number of sports are ready to go -- even hosting "test" competitions.
And Athens itself is being remade: a brand new airport, a refurbished subway system, and new highways. There's also a major effort to beautify building facades and public squares.
"By the time the Olympics occur, this nation will have spent over $5 billion," says Rondos.
"A lot of things changed radically in the last years. We are not the poorest anymore. We are a stable democracy. And we are an extremely good place for people to invest, so having showed that we are able to do good Olympics, it will be the turning point for Greece," says Bakoyanni.
But success won't depend just on finishing the construction. Even more important, and far more serious, is the issue of security -- making the games safe.
"When we took on the Olympics, 9/11 hadn't occurred," says Rondos. "Since 9/11, we have all collectively, internationally, discovered the nature of a new threat."
That threat is al Qaeda, and its network of offshoots around the world – things that Bruce Hoffman studies at the Rand Corporation.
"Al Qaeda, especially in the post-9/11 world, is intent, I think, in rejuvenating or regenerating itself," says Hoffman. "And it has, I think, this abiding faith in the power of the spectacular that would be their attention on the Olympics."
"Also, isn't it true that the Olympics really is kind of 'the Western world,' 'the civilized world,' everything they hate?" asks Stahl.
"Oh, absolutely. Especially the Olympics being in Athens. Being in Greece. The cradle of Western civilization. The embodiment of Western values," says Hoffman. "That makes it an enormously attractive symbolic target. More so, perhaps, than ever."
No one can accuse the Greeks of taking security lightly. They'll be spending a record $1 billion dollars on the effort -- three times what the Australians spent at the last summer games. 50,000 security officers and military personnel will be on guard.
And they may need every one of them. Greece literally sits in the middle of much of the world's trouble: the Balkans on one side, Turkey and the Middle East on another, and hundreds of miles of porous land and sea borders.
"When you have that length of border, and especially that much of sea coast, it presents special security problems, of terrorists, as it were, coming in beneath the radar," says Hoffman. "There has been a number of incidents over the past three decades that have involved Middle Eastern terrorists that have seen Greece as a crossroads to carry out terrorist attacks."
When you look at a map, it appears impossible to keep everybody out since there are so many avenues of entry. "The security plan, is, has taken all of that into account," says Rondos. "There will be a capacity from our allies that will exist to interdict anything that looks as though it may be coming in our direction that we think is suspicious."
When referring to allies, Rondos says he means the United States. In fact, Greek and U.S. forces recently concluded joint military exercises. And Greece needs all the security help it can get. Only a few years ago, a U.S. government report singled it out for being lax in fighting terror, and just last summer, U.S. officials were horrified at the screw-ups during a Greek security exercise.
"One of the incidents or lapses that was most widely reported involved a woman pretending to be pregnant who actually was carrying a bomb and nevertheless was able to pass through security," says Hoffman.
"Now, that's viewed as the most elemental, I mean, the most basic kind of threat, and I think that generated concern that perhaps security .. well, certainly that security had to be strengthened, and that really the expertise of a wide variety of countries who have had long experience in countering terrorism - not only that, considerable success - could be usefully enlisted."
Now, Greece has even asked NATO to help with Olympic security. The request was made one day after last month's train bombings in Madrid.
"Honestly, we don't feel alone," says Bakoyanni. "We feel that NATO, the Americans, the Israelis, everybody around the world is collaborating for the security of the Greek Olympic games."
It's not just a matter of protecting the games, of course, but the entire city, including a port where 11 huge cruise ships will be used as floating hotels.
"We saw that in the Atlanta Olympics, where the venue itself was very well-protected. But the freedom park, next door, was where, precisely for that reason, the terrorist sought to attack, and to detonate his bomb."
U.S. athletes have even begun expressing their fear that they'll be in the bulls-eye in Athens.
"With all due respect to the athletes, they might want to spare a thought for everyone else who lives in this city and all those who are going to come here to watch them," says Rondos. "Everyone's in it with them."
One adversary Greece feels it won't have to face is a homegrown terror group called 17 November, which waged a three-decade campaign of assassination, killing U.S. and British diplomats and Greek politicians -- including Bakoyanni's husband, who was shot and killed in Athens in 1989.
17 November operated with impunity until 2002, when its leaders were finally caught after an explosion led police to their hideout.
"We were lucky. Probably one of the 12 gods of Greece decided to do something about it, because the bomb exploded in the hands of a terrorist," says Bakoyanni. "We don't have any worry about domestic terrorism anymore. And I'm really glad, because if you asked me two years ago, I would not be able to tell you the same answer."
But Greece is still vulnerable to foreign terrorists. Stahl told Rondos that Sports Illustrated reported that if Sept. 11 had happened when the IOC went to select Athens, they couldn't have picked a worse city in terms of terrorism.
"I take the completely opposite view. I'm gonna be at these games, and I'm gonna be there deliberately because it is post 9/11," says Rondos. "I'm gonna get in the face of the terrorist who thinks I should go and hide rather than have the Olympics in their birthplace. If we go the logic of saying 'This is not the ideal place,' well then, what is? What is?"
Greece still has to deliver a safe Olympics. And, they also need to deliver that blasted stadium roof.
"It's the moment where Greece will be branded in one way or another," says Rondos. "This is the challenge we face. If it goes well, everyone…you, everyone else will say 'By golly, they pulled it off. And you know what? I'm gonna go back there again.' The alternative is, 'The Greeks didn't get it right.' And it will mark us. It will be a stigma for a long time afterwards. And we all know that. That's the challenge we face."