It looks like the Japanese hostages will be freed, instead of being burned alive by their kidnappers. That's good news, extremely good. It may not stem the controversy over what happened, though.
Japan's presence in this particular conflict has always been problematic at best. The Japanese people were extremely opposed to sending over GSDF forces to Iraq, and I've got the impression that even the government would have said "no" had Bush not leaned on Koizumi to send some sort of help. The eventual compromise position was that the Japanese would go over, but would operate strictly on a humanitarian basis. They'd only use their guns to defend themselves. There was, and is, a controversy over what would happen if Japan lost soldiers and/or civilians, and we've come very close to seeing what would happen.
I've thought about it, and I think that there are really three ways it can go. First is a broadly "right-wing response", which will be overwhelming outrage at the deaths of Japanese in Iraq and a call for either an increased presence in Iraq and more aggressive rules of engagement. It would almost certainly be used as ammo for the right's crusade to end the section of Japan's constitution that outlaws war, which has been seen as outdated (if not humiliating) by the Japanese right for a while now. That'd almost certainly get blended together with a nice helping of xenophobia and anti-foreigner anger: at the Iraqis for killing Japanese, and at the Americans for forcing Japan's hand.
The more likely responses, however, are broadly left-wing, and they're a touch more interesting. The simple response is almost certainly the most likely: "let's get them out of there, I don't care how and damn the consequences". Unlike the United States, there isn't much support for their presence in the first place, and there's a conflicted attitude towards the military in general that makes appeals to "our troops overseas" unlikely to gain much traction. If Japanese citizens were to die in Iraq, it's quite likely that Koizumi would listen, and pull Japanese troops out. Even if they don't die, he may do so anyway if the current uprising is not quelled by the Americans.
The third option, however, is the one that is either the most interesting or the most disturbing, depending on how you look at it. Let's say Koizumi says "no, we can't leave, the Americans would punish us for it and we rely on them for their security". This is actually quite likely to happen. Some people will undoubtedly conclude that Koizumi is lying, but others will conclude that he's right- the Americans have the Japanese by the proverbial short hairs and there's nothing that Japan can do about it. What if some people say "Ok, then, let's get out from under the American umbrella and start handling our own affairs?" This isn't necessarily a right-wing response, because some on the left will almost certainly realize that the United States is going to be able to continue to dictate Japan's foreign policy as long as they're protecting them, and that Japan's freedom to remain broadly peaceful requires Japan to become responsible for its own security. There is also an economic argument to be made for Keynesian stimulus through military spending.
If that happens, Japan would almost certainly scrap Article 9 (the article that forces peace). If the left decided that pacifism is impossible as long as they're under the American umbrella then there would be little real opposition; the right certainly isn't going to oppose them. A Japan with a real military wouldn't really require the United States' assistance- they're already surprisingly powerful using only the constitutionally mandated 1% of GDP, and have leveraged their technological prowess into creating one of the best-equipped militaries in the world. They may have a small (and shrinking) relative population to other military powers, but you don't need a huge population to have an effective military.
If this happens, however, the strategic situation in the Asian-Pacific region would change overnight. China would almost certainly freak out, as Japan's technological prowess easily dwarfs their own. North Korea would likely do the same, but Japan's potential military capability really dwarfs their own; the only reason it doesn't now is because of that 1% of GDP limitation. Both have nuclear weapons, but Japan could easily build nukes as well, and public opinion on that issue is coming around thanks to the threat of North Korea. South Korea would be strongly opposed, but Japan isn't really the same country it was during the Meiji period; the obsession with invading Korea that plagued Japanese foreign policy since the late Ashikaga shogunate would be seen as ludicrous nowadays. In a lot of respects they're actually natural allies against China and North Korea. All the players in the region must also be thinking about the possibility of China flying apart into smaller statelets; the communist party can't last forever, and the centrifugal political and economic forces in China never really went away.
It would be deeply weird were the United States' actions in the Middle East to prompt this sort of massive change in East Asia. Indeed, the news that the hostages will be released implies that this scenario is farther away than it seemed yesterday or the day before. Still, the central contradiction of Japanese pacifism has been around for a long time, and Iraq is just as possible a catalyst as any. It's not like being an "economic tiger" is going to do it anymore. The 90's are long dead.