Hi there,
I also work full time (I have a 4 month old son), and we have been implementing Your Baby Can Read since day 1 (litterally). While it may be slightly different from the Little Reader (we will start on that when he is 7-8 month old and really starts making progress recognizing words), the principle is the same, as far as being diligent showing the multisensorial materials. I have a nanny, she has a schedule that she has to follow (we show the video twice a day - I do the first one early morning, she the next after lunch- , and during a 3rd session - about 4PM, she shows books and flashcards). As long as you trust someone to do it, it is not complicated. you just have to make sure that this is interactive (i.e. she doesn't plop your child in front of the videos without adult participation), but it is less of a problem with the little reader because you have to be there to forward slides. The night before, I set out the exact material I want her to use for the next day. On the week-ends, we focus on books, so he gets a break from these.
In general, with the nanny, I limit the availability of implements that are more for baby-sitting (like bouncers, bumbo seats, etc) and that decrease the need for one on one attention and don't do much for physical development.
I hope this helps.. please don't hesitate to recontact if you need more info