That is the wonderful thing about the breathing, and the reason it is such a helpful object of attention. It is both perfectly ordinary (we are all doing it, all the time) and extremely special (if we weren't doing it, we'd be dead)... Everybody breathes. It is also extremely portable. We take it everywhere we go. So if you choose to practice with the breathing, it has the advantage of always being there. No matter how many times you forget it throughout the day, you can always take it up again. There's another in-breath. There's an out-breath.
Sometimes people think that when we speak of following the breath throughout the day, we are exaggerating for effect. We really can't mean such a thing. And maybe there is no one who can be mindful of every breath throughout the day. It is also true that there is a great deal of temperamental difference among practitioners. Some people who like to follow the breathing while sitting do not like to follow it in other postures, and that is all right. It is meant to be an aid to mindfulness, not an impediment. If you are better able to be mindful without it, fine.
Yet you really can't know until you make a sincere effort. One thing that many students find is that the more they pay attention to the breathing throughout the day - while eating, washing the dishes, listening to music, walking in the woods - the easier it is. The capacity to stay with the breath gets stronger and stronger, and the breath itself becomes more vivid and available and alive. It doesn't do much good for me to say that, of course. Really to discover it, you have to try it.
When I first worked at training myself to be mindful throughout the day, I was using mantra as my meditative support. And I decided on certain prompts, cues, in the environment to help me. Fastening my seatbelt was one. Looking at a time piece was another. Any sudden noise like a siren was still another. I recommend that you pick reminders in your environment that will help bring you to mindfulness. Then try using breath for your support as Rosenberg suggests. Sound will also work quite well as a meditative support throughout your day. Give either one a try. The equanimity that is cultivated through such a practice is very stable and reliable.