Ivy league, and other prestigious schools, offer two things that I would say are most important: Opportunity and resources. Opportunities are often in the form of more diverse course choices or more internship/research/project opportunities. If an Ivy league student doesn't utilize those, they are no better off than a student coming from a less recognized university. Believe me, there are plenty of those students leaving even the best schools, and plenty of incredible students coming from lower ranking schools. I think most recruiters know that and often disregard the title on the degree, at least once the first round of candidate selection has been done.
The important part of going to college, no matter what school, is to get the most out of it. Work hard to be a good student, but you don't have to be the best, that's not the only goal. Try new interesting subjects, get involved with teams or projects, challenge yourself.
Finally, I highly recommend looking into transferring schools, if you don't get into the "best" one your first year. This is really the smart way to do it. Those advantages I talked about for the "good" schools? They matter way more your 3rd or 4th year. Get your core curriculum done at a cheaper, "easier" school and be top of your class, then, transfer into that expensive or difficult school and get the same diploma as everyone else.