It depends on your state.
Some states have 100% tuition reimbursement, based on the cost of the state's university system. If you were to go to a state school, your tuition reimbursement combined with additional benefits (such as the GI Bill) will come close to covering everything. If, like me, you go to a private school, you will be responsible for the additional tuition.
I know of no state that directly covers all the expenses of going to a given school--if anyone else knows, they should chime in.
In short, it depends on your state. Contact your education benefits coordinator--or, if I read between the lines correctly and assume that you have not enlisted yet, find out what type of program your state has.