I'd be willing to bet most of the people who say it cannot be done don't know too much about homeschooling/cyberschooling. I have 3 in cyberschool, one infant, a writing business, a small blueberry farm, and rental property to manage. Let me tell you about my day.
I get up at 5:30 am, throw a load of laundry in, and by 6 I kiss my hubby off to work. Then I sit, sign my kids into school before they get up, and work my freelance writing job for about 2 hours. By this time my 1 year old is ready for her morning snack.
I get the kiddos up and feed them breakfast, sometimes my 9 year old will do this for me, especially if I'm on a deadline and need a few extra minutes. By 9:30 we are ready to do school. I choose a student to focus on, and let the rest do supplemental activities such as computer learning games, worksheets, coloring sheets, ect. I work through the curriculum with that student until lunch. We usually get done with about 2 or 3 days worth of work in the morning.
We eat lunch, baby gets another snack and heads to bed for her nap. Depending on what we got done in the morning, I let the kids go and play outside the rest of the afternoon, or let them do an art project or science experiment in the kitchen. This gives me some time to make calls to contractors or write another article. If we didn't get very far in the morning, we go at it again until we've finished at least 2 days worth of work.
The end of nap time and dinner comes rapidly. Hubby comes home, we enjoy a meal together and then head off to an activity or a property (yes with all 4 children) and do some work.
This way of life is different from the "send your child off to school" life. I was bored while my now 4th grader was in 3 year old pre-school (actually she was too!). I spent money we didn't have and ate lunch out when I didn't need to. Now, we eat almost all home cooked meals, and I am never EVER bored.
Can it be done? Yes, and what an exciting ride it is. :)