Vox Day writes the article I was going to get around to, which is that the idea that the Japanese could have mounted any sort of significant invasion of the continental USA was ludicrious, even at the time. As Day does, I find it difficult to believe that anyone could take the idea seriously. I’d add that even the Japanese would have known this, their own nation having been saved from invasion by the difficulties of resupply over the ocean (from whence “kami-kazee”, divine wind). All of this concerns Michelle Malkin’s book about the internment of Japanese in the USA during WWII. Whatever security risks there may have been from the Japanese in country, support of an invasion wasn’t one of them.
In the comments to the original posts are questions about long term Japanese war aims. These were not invasion of the USA and probably not even the invasion of Australia. Instead, the goal was to seize a large chunk of south east Asia with a defensible perimeter, making it too expensive for ANZUS to break through. This was the “Greater East Asian Co-Prosperity Sphere”. In many ways it resembled Confederate strategy in the War between the States and ended badly for the other side for much the same reasons.
Interestingly, the Doolittle Raid may have actually played an important part in defeating the Japanese grand strategy. After the raid, there was such a panic (despite the completely negligible damage) that the Japanese extended the perimeter, weakening it and themselves. It’s not only democracies that are susceptible to such panics during wartime.