Is it possible for active people to truly live practice "mindfulness"?

Several buddhist/meditation books recommend me to practice "Mindfulness" or living in the present moment alone. I am a married man with a 4 yr old son and wife.I am currently working in one of the top 10 IT company in the world. On any given time I will have a "list of things to do" which are important and which are pending from my side. So if I ignore my tasks and "live only in the present moment" it will greatly harm me and my family's life. Also how am I supposed to be at peace when all the pending items keep reminding me that they are not yet completed even if I try to calm myself for couple of minutes. Does this mean that people with lot of responsibilities should refrain from practicing "mindfulness" ?