volvie-
Out of the 25%, probably half of them could do it if they strained themselves the way people are straining today. For the other half (including kollel, rabbinate, or other families with lower income) if there is no scholarship money available then they are forced to solicit funds directly. This too, is no different from the obligations that schools place on their parent body except that in this case most parents would be exempt.
Personally, I think donations would be plentiful, even from tuition paying parents. Think about the upper 25% instead of the lower 25. These families are either high income or families with few children and decent income. They are probably comfortable enough and happy with the tuition levels so that they would voluntarily want to help the lower 25. Plus there are alumni, grandparents, and businesses who will all look for tax deductions from time to time. This model can work.