This book is great - so great that it's kind of sad that I can't recommend it as heartily as I'd like. This is because of two problems: one, pronunciation, and two, the katakana section.
Other reviews detail Heisig's method for memorisation, so I won't go into that - except to say that I found it really helpful, and I would have undoubtedly found learning much harder going if not for his help. I could indeed learn the hiragana, as promised, in three hours - although spread out over a week, and I'd say it took me a couple of weeks to be confident in reading and writing at a reasonable speed. Ditto the katakana.
The main problem is the pronunciation. Even if we take away the issues caused by the American accent vs. the English accent, you're still not going to get a sense of how to pronounce things correctly if you go by the keywords. It's really easy to think `oh, the keyword for `ko' is `comb', so it must be pronounced like the co in comb' - but it's not. `Ko' is pronounced more like the co in `copier' or `cough'. Even said in an American accent, the co of `comb' is not going to sound right. Of course, this is not a problem if you're taking a class and or can get a native speaker to teach you the correct pronunciation, but if you're unfamiliar with the sound of Japanese and this book is your first exposure to it, you're going to pick up some bad habits.
A minor problem is the katakana section - which you do second. Heisig didn't write it himself, someone else did, and it's poor quality. Too many of the entries say `it's just like the kanji'. Since it's unlikely that many people will know kanji but not know katakana, for the majority of learners that's just a really irritating thing to say. However, if you've done the hiragana section (which you will have), then you can easily make up your own stories for those entries which are inadequate.
In conclusion: I found this book really, really helpful, but I already knew how to pronounce the kana. If you don't, then this book can still be of tremendous help, but be very aware that you can't go by the pronunciations in the book.