Both sides are guilty of posturing.
In other news, the CCP placed a rather convincing add in the NYT detailing exactly why they deserve those islands. I'm slow to take China's side due to, ahem, ideological differences, but they at one time and for a long time had control over those islands. Whether or not these claims are valid is beyond me, but remember Japan has invaded China at one point, making many of their land disputes hard to resolve.
Further complicating the issue is Japan's dire need for resources. They are an island nation whose main resources are impressive exports, they need natural resources very badly. And since the US is Japan's main muscle (have been since WW2), they are relying on us to back claims that the island is THEIRS.
So we are caught between a rock and a hard place. On one hand we risk strained relations with China, who while a growing threat are currently not very threatening. On the other hand, if we supported China, that would be going against months of campaign rhetoric and hurt our island friends of Japan. No winning there.