I concur with TPM - you should know what the offer is and what costs to expect before committing to spending whatever amount remains. When my son was made an offer (non-P5 D1), the coach described the scholarship in terms of the 1st year. So I asked what happens in years 2-4 and he told me that the scholarship amount would be the same in those years. Then I asked how many players graduate in 4 years. His answer was "Not many, so if your son needs 5 years to graduate I'll pay for that too".
My reason for asking was not to negotiate, but to clarify and understand what we might be getting into. I don't think it came across as pushy or entitled at all. But then again, I think it is foolish to order the restaurant special without knowing it's price.