I am wondering about the feasibility of working part-time during a full-time MBA program. I would like to apply for top business schools like Michigan Ross and Duke but I simply cannot afford the costs. Working would allow me to make some extra cash which would go a long way towards affording the programs.

No, that's just not going to happen at a top-tier school. They won't allow it, and you just won't have the time. When you are not sleeping, you'll be studying or networking. Save, borrow and apply for scholarships.

I am not sure about Ross and Fuqua, but I know that NYU Stern offers students opportunities to do teaching or graduate fellowships; students can be admissions ambassador, teaching assistants, or career coaches. By doing this you get something like $20,000 towards your tuition; that's nothing to scoff at but it also depends on how much of a time commitment it ends up being.