I'm a grad student at a big-10 university.
I eeked into the program. My grades were good, but not very competitive for the program. For the first semester, I paid with Federal Student Loans.
However, I had meetings with the academic program director. He knew my name and situation, and I think this helped me secure a teaching assistantship. That is currently how I'm paying for school in this, my second semester.
I've since applied for an NSF fellowship - if I were to secure this, I would have my research, classes, and living expenses paid for by the government.
If it doesn't, I may have a good shot of gaining a research assistantship through the connections I've gained within the department.
I would say if you have a brilliant resume, and existing connections within the institution to which you are applying, then you should pretty easily get an assistantship. Otherwise, I recommend that you speak with the program director as ask him/her "What can I do to increase my chances?" Also, ask about fellowships you can apply for.
Of course, you can pay for the whole thing. If you don't mind, then there is nothing wrong with that.