Need-based aid means they calculate an estimate family contribution, then subtract that from the cost of attendance. The rest is your "demonstrated need," which they give mostly with grants, and some self-help (loans and/or work-study, but the loans are usually federally subsidized and they recently instituted rules that strictly limit how much loans they give. I believe incomes <60k or something like that do not receive loans, only grants). theoretically, if your family was determined to only be able to pay $750, you would receive $54,000 - $750, mostly in grants with some work study.
Is that family contribution your FAFSA estimate? since they'll make their own calculation, what they consider your EFC is the real variable here. but either way, assuming you have no other assets, you would probably be looking at a very generous package. look here, especially the last few examples:
Wesleyan University : Admission