There is no answer to that question. The more time you put into learning Japanese (using the most efficient study techniques) the faster you'll learn it. Also, worrying about how long it takes isn't really productive. It's better to just study every day knowing you'll be fluent eventually.

The Japan American Society of LA (runs the Japanese Language Proficiency Test) claims it takes 900 hours to become "fluent" (level 1 of the JLPT), as you will find by a few seconds of searching on the WWW. In contrast, an article appeared in the Wall Street Journal many years ago, which based on college surveys, said that about 1000 hours were required to learn "basic" level Japanese. Basic here refers to the standard college level classes normally taught over 4 semesters which include about 40 basic grammar patterns and a vocabulary of about 2,000 words (about 1/2 that of normal conversation). Note that this level of difficulty is about 4 times that of learning an ultra easy European language like Spanish. Also a little calculation indicates that most students are not actually putting in the time (1,000 hours) to learn basic Japanese. That is to say, they are not spending a hour+ per day repeating grammar drills, listening to tapes, etc., which helps explain why so many students have such dreadful pronunciation and can't carry on a basic conversation. Of course, it is very productive and important to realize how much time this takes, since you need to use efficient study methods and need to learn how to budget your time to get anywhere.