I really wish I were able to post links. There is a lot of good information out there.
Fairly crude weapons can be built without testing, but they're heavy (thus harder to launch) and of "moderate" yield. Keep in mind that the weapons used on Hiroshima and Nagasaki would be considered tactical today. Japan could likely build an arsenal fairly quickly, but I doubt it's a matter of "days." American weapons of the "Fat Man" type took something like two weeks to assemble from warehoused parts.
For a look at an estimate (obviously speculative, but based on a lot of research) of the effects of a strategic exchange with the arsenals that existed in 1988, look online for "Johnston's Archive Nuclear Weapons" in which you will find "The Effects of Global Thermonuclear War." It estimates 400,000,000 dead on the first day and 1,850,000,000 a year later (mostly from starvation and disease resulting from a shattered global economy).
That assumed 4,790 megatons from the US arsenal and 13,300 megatons from the Soviet (with 662 from other arsenals). Note that as of 2007 the estimated arsenals of the US and Russia were still 1,520 megatons and 5,480 megatons respectively.
The Cold War was simplified by having only two major players. As the stockpiles grew and the stakes became higher, they became very careful not to push each other into corners. The Cuban Crisis of '62 was probably the closest they came to losing control of the situation. The US indeed came close to striking and perhaps invading a nuclear protected country, and it is now known that Soviet forces in Cuba had already been given the access codes and ordered to retaliate with nuclear weapons if they had.
The British, French and Chinese arsenals were all MUCH smaller, but their existence added new dimensions in any crisis. They were built because of lingering doubts that the US or SU would stand up for their partners faced with such a threat and also to give themselves more room for an independent policy. This is especially true of the PRC, who broke totally with the Soviet Union over the issue (among others).
However, this led to what was called the "N-th Country Problem." In a crisis involving A and B, each has only the other to fear. A can plan his actions based only on how he thinks B will react. However, if country C also becomes a nuclear power, A must now consider how both B and C will react, how B might react to C's reaction and vice-versa. This is a major complication even if C's arsenal is small, as the fear is that it makes situations involving the big arsenals more unpredictable, and it snowballs with the number of players.
Having a large number of fingers on a large number of buttons thus may well undermine deterrence rather than strengthen it. This is why even the most hawkish of analysts came to see some kind of arms control as necessary. Some estimates from the '60s imagined twenty to fifty nuclear arsenals by the '80s, and that scared even Dr. Strangelove. Neither power liked even their oldest and best allies joining "the club."
Several states have, since then, decided to arm openly or semi-covertly. Some do so because they fear a regional rival, others because they want to replace a lost nuclear umbrella. North Korea, in my view, has also found it a convenient way to twist the lion's tail.
Actually getting such weapons is a two-edged sword though. It does make other nations think twice about messing with you, but it also makes them pay VERY close attention to you. Rattle the sabre too loudly and someone may decide to pre-empt, and if there is a global exchange you can bet you'll be hit whether you were directly involved or not. No doubt many other factors were involved, but note that the rhetoric of both the Soviet Union and PRC mellowed after they got nuclear weapons.
A small nuclear arsenal is a little like having a knife. A guy without one will back down, but another guy with a knife may not, and a guy with a gun most likely won't. I suspect the Japanese leadership would have to feel really cornered before they went that route, but if the non-proliferation system continues to erode, who knows?
It would be not beneficial to the US if China were to become democratic and understanding and supportive to Japan.
