I would say 1 month is not enough time. You will need to read the entire HFS&J book once thoroughly, going thru all questions and exercises, and then at least a second time to review the content. Granted, the second time goes much quicker but it is invaluable at refreshing your knowledge and fine-tuning it. I believe it will take you a month to get thru the book the first time.
Additionally, once you feel you are ready to take the test, you should spend a week taking practice exams. Each exam can take 2-3 hours and you still need time to review material on missed questions. Finally, plan on putting at least 5 hours into the HFS&J final exam, since it is the hardest one you will encounter, and will require the most review.
Also, don't forget to study the other resources you'll find mentioned on this website. (Powerpoint presentations helping with memorization and notes on topics that aren't completely covered in the book like dynamic attributes and Peabody's notes on Design patterns)
I think you could get it done in 5-6 weeks, but you'll still need to be focused. If you have past thorough experience with Servlets, JSP, EL, etc you could probably get it done in a month.