From what (little) I know of Japanese culture, hostage-taking and threats aren't likely to weaken Japan's resolve.
Iraqi militants are today threatening to burn three foreign hostages to death unless their country quits the US-led coalition.Perhaps my brother can give us more insight on the situation, since he's studied Japan extensively.
Two Japanese men and one woman are being held by a previously unknown group which has vowed to kill them if Japanese soldiers do not leave Iraq.
Prime Minister Koizumi fought hard to get Japan's Self-Defense Forces (SDF) into Iraq, and for him to back down in the face of direct threats to three individual lives would be a great loss of face, as it would be for any national leader. More than that, by backing out he would be bringing shame to the nation, a gesture that would be unacceptable to any politician in hope of retaining popular support. And although Koizumi is elected by the Parliament, his PR strategy and wide-spread popularity in Japan are the roots of much of his power. So, he would not do something that would bring shame to so many, for it would undermine the major source of his influence.
Also, it is important to remember that there are several possible reasons that any individual member of the Japanese Parliament might want the SDF in Iraq. First and most persuasively, the Japanese economy is quite dependent on favorable and cooperative relations with the US. Withdrawing the SDF from Iraq for the sake of three lives would certainly harm US-Japan relations, though not irrevocably of course.
Second, for politicians who personally support an amendment to Article IX of the Japanese constitution to allow the development and deployment of a national military rather than simply a Self-Defense Force, pulling the SDF out of Iraq in response to a relatively small, though gruesome, threat would greatly undermine the political strength of the pro-military position. That is, sending the SDF to Iraq was a great DOMESTIC political victory for those Japanese who support the development of a full-fledged Japanese military, and to remove the SDF because of this would show an awful lack of resolve that would turn domestic political victory into political defeat.
Third, those Japanese members of Parliament whose constituents favor the development of a national military, along with all the economic and social consequences that a strong and growing military entails in a capitalist economy, would put great pressure on PM Koizumi to keep the SDF in Iraq, for reasons similar to those given above.
Fourth, organizations in Japan interested in high-tech research and development, including many private firms, government-sponsored research institutions, and bureaucrats within a wide range of ministries would all apply pressure to maintain the SDF in Iraq. Again, the incentives to do so can be traced back to the hope for an eventual constitutional amendment that would allow Japan to develop a full-scale military, and to the fear that backing out of Iraq now would undermine that cause. The ministerial bureaucrats especially exert considerable influence on members of Parliament, as the two groups have a highly mutualistic relationship. And since increased government spending on a full-fledged Japanese military would mean that some bureaucrats somewhere in the Japanese ministries would be controlling more resources than they did before, there will be ministerial pressure on Parliament to keep the SDF in Iraq now.
Lastly, there may be Japanese who sincerely support the moral cause in Iraq and the War on Terror, and though the pressure applied by this group will be important in the decision to keep the SDF in Iraq, this group of moral supporters is itself hard to classify or identify in any simple way.
I doubt the SDF is going anywhere, for a while. If it does, it will be the result of several humongous political mistakes.