I would like to say that mantras do work, but they take work like anything worth while in life! There is no such thing as a free lunch whether we are talking about economics or mysticism.
The author says to do a 40 day discipline with the minimum 108 repetitions, notice the word minimum.
108 repetitions will yield mediocre results at best, and no results at worst. I have done quite a few mantra disciplines and doing 108 a day in most cases is not going to cut it.
Think about it, what if you did the absolute minimum in any given task in regular life, would you expect maximum results? Use your logic, if you did the absolute minimum in school you probably won't get into college even though you went to school EVERYDAY! If you did the absolute minimum in your career you probably won't get promoted or it would take much longer than it should had you had worked harder and tried your best. What if you wanted to get in good shape and you did the absolute minimum amount of exercise and ate the minimum amount of healthy food, would you expect spectacular results!? OF COURSE NOT, only a fool would think other wise!
This is EXACTLY the same with mantra disciplines.
According to traditional texts on sanskrit disciplines in order to get a mantra to work best there are 2 ways.
One is to receive the mantra from a guru or pundit. The reason for this is that those who have unwrapped the power of a mantra through many repetitions achieve something called mantra siddhi. This means that they have attained some measure of power and proficiency with the mantra. At this point, they may give a mantra to others as an empowerment, meaning that the recipient will achieve results faster than doing it without having received it without power. This is very similar to receiving shaktipat from a guru or siddha, or being born into a rich family. You have to work A LOT less harder to get results.
The second option where most of us fall in is to attain mantra siddhi ourselves since most of us here in the states to not have access to a fully trained pundit or guru. According to traditional sanskrit texts as a general rule the minimum number to achieve mantra siddhi is 125,000 repetitions for any mantra.
I would suggest that you do a 120 day discipline if you are really in a bad situation. Your goal should be to unpack the power of the mantra and attain mantra siddhi. If you do about 10 malas a day for 120 days that's 129,600 malas, enough to attain mantra siddhi for most mantras. This level of devotion has ALWAYS yielded results for me usually before the discipline is completed.
They don't call it bhakti (devotional) yoga for nothing, it takes devotion to truly make it work.
If you are lazy my last suggestion is to get a lakshmi kubera yagya/homa. In a yagya a group of highly trained pundits with mantra siddhi will recite mantras on your behalf in an elaborate ritual. For this I would suggest going through a reputable group like Amrita Puja.
The moral of this story is if you do the minimum you will get the minimum.