How much should I chant? Does chanting Nam myoho renge kyo work?

First, everyone is different, some of the Japanese ladies use the little daimoku charts where 15 minutes equals a tiny square of a huge picture...etc. You try to set a goal it sounds like of x minutes per day. This also leads in my second point, which is that I do not believe that chanting itself is necessarily a "good cause". I say this because.... what IS the Gohonzon? It is the actual manifestation of Ichinen Sanzen, and we seek Kyochi Myogo in our practice.

That is, a fusion between our life and the perfect blueprint of life which is "Gohonzon". So back to the point: Within Ichinen Sanzen, cause and effect is explained in detail. The Ten Factors ("Ju Nyo Ze") make it clear that it is the NATURE of a cause that matters, not the cause itself. This would indicate that the act of chanting itself has no value, positive or negative. It's value rather would be determined by one's motivation or nature in that cause of chanting the daimoku.

What if in my head as I chant, I curse this Buddhism? Is it still a good cause? How about those who appear to betray Buddhism, yet chant... are they making a good cause when they chant in anger and pray for the Gakkai to die? Think it over.... It is always the NATURE of a cause that matters and thus creates an immediate latent effect which will manifest in time.

This leads to point 3: QUANTITY of daimoku, in my opinion is irrelevant. It is sincerity that matters. One sincere daimoku is more valuable than a million careless daimoku. The opposite is true as well, Nichiren Daishonin states "1000 pots of laquer can be ruined by a single crab leg". Which I believe indicates that every single cause counts and ones destiny or "karma" is constantly accumulating.

Anyway, just wanted to share my thoughts on it and especially stress the Ten Factors as they are very fundamental to how our life conditions change (ie how we interact with environment and have influence over it and it over us) which is the main point you seem to be trying to make. The damoku is indeed the "One Essential Phrase" as Nichiren Daishonin puts it, but I do believe that faith is the key to making it awaken one's Buddha nature. NOT the act of chanting itself, but FAITH.

A last thought: So I suppose it's like this: If I have a bike, if I don't know how to ride it, it's not going to help me get very far. I just don't see much value in chanting without faith.  Otherwise, anyone who chanted could not be deluded... yet we know that is not the case. I do not think one can awaken Buddha Nature without chanting, but I also don't think chanting works without faith and sincerity.