Not to discourage other answers, but /u/notbobby125 actually talked about that in this recent thread.

There really is not any evidence for the alleged letter mentioning "blade of grass," and there are serious doubts that it existed for two reasons.

One, the letter allegedly came from the files of Gordon Prange. He was a historian assigned to MacArthur's staff for the occupation. These duties brought Prange into contact with a number of surviving Japanese officers, which was an important connection for his postwar career as an author of a number of books on the Pacific War such as At Dawn We Slept. While this might appear to give Prange a degree of veracity, his histories are somewhat problematic at places. He had a tendency to take his interview subjects at their word and perpetuated a number of myths such as the vulnerability of Pearl Harbor's oil reserves. This is particularly true of his accounts from Japan. Although I am not a 100% certain on this, I am fairly sure Prange did not speak Japanese, or fluently enough not to rely on a translator. Nearly all the Japanese sources in his books cite Japanese individuals like Chihaya Masataka who provided Prange the documents and translated them for Prange. The January 1941 letter to Sasakawa Ryoichi in which he claimed that peace would be certain if we marched into the White House came from the IJN lawyer Juji Enomoto. This is not necessarily bad, Japanese is a difficult language to master, but it did allow some individuals to put out their own self-interested claims with relative impunity. The Pearl Harbor flight leader Fuchida Mitsuo told a number of tales such as the abortive third strike on Pearl or the Japanese carriers a Midway being on the verge of launching their planes before being destroyed. None of these narratives appeared in the immediate postwar interrogations and the often originated with Fuchida in the 1950s and Prange repeated them. IJN officers, much like their German counterparts, were very self-interested in producing a self-exculpatory explanation for their defeat in the 1950s. Prange did his part in perpetuating these mythologies.

The second reason to be highly skeptical of this quote is that neither the IJN, nor anyone else in Japan's military and state hierarchy, were envisioning an occupation of the mainland US. The overarching goal of Japan in 1941 was to secure what Japanese military planners termed the Southern Resources Area (SRA). The SRA consisted of the Philippines, SE Asia, Indonesia, Borneo, and possibly parts of India. The overall rationale behind this was that the SRA would allow Japan near autarky in terms of natural resources such as oil or rubber. Concurrent to the Japanese seizure of the SRA was the expansion of Japanese bases into the Pacific to form an iron-clad defensive perimeter that would prevent the Americans from retaking the SRA. The Pearl Harbor raid's main objective was to prevent the USN from interfering with the seizure of the SRA. The hope among IJN planners was that the defensive ring would enable the conditions for a decisive naval battle to occur. Peace would then occur after the battle had been won and the SRA would be harnessed for Japan's regional power and Nationalist China would come to terms being blockaded from all sides. Further Japanese expansion might occur in India, Australia, or (most likely) the USSR, but not California or Oregon.

This context is pretty vital to understand Yamamoto's statements like his January 1941 letter to Sasakawa. While some nationalist hotheads envisioned an easy victory over the US, the IJN anticipated a very tough campaign against the US. While they were incorrect about both the efficacy of their defensive barrier and the IJN elevated the idea of a decisive battle to near cultlike proportions, the IJN chiefs still thought war against the US was a difficult proposition. Any moves to expand Japanese power beyond the SRA and the defensive barrier often entailed bitter fights between the services and operations like Midway had to pass significant hurdles before their approval.

All of this makes the gun advocates' use of the "blade of grass" letter somewhat obscene. For one thing, the letter has never been verified to exist; it does not really come up within the historical literature independent of gun control debates. Now Prange's papers are available at the University of Maryland and Enomoto's are at the Institute for Defense Studies in Japan, but nobody in these debates looks for them. More often than not, gun advocates just do not care if the letter exists, such as this letter to the editor which downplays the lack of evidence for the letter and states:

After all, [the letter] either does exist or it doesn't. But the facts remain. Japan did not invade the U.S. mainland after Pearl Harbor. And we were armed.

So I stand by the Yamamoto quote, and leave it up to the reader to determine its validity. But I personally don't see a problem.

This is a very lazy way to do history. Japan did not invade the US mainland because there were no plans to do so, even over the long-term. The fact is no serious Japanese military planner was envisioning an occupation of the mainland US. Private ownership of guns was completely irrelevant to Japanese calculations which were more predicated on existing military strategies and bottlenecks in their military capabilities such as shipping.