As a person who was not at an Ivy league school who was accepted to some top programs including Harvard, I back what this statement about letters of reference. Additionally important is senior level coursework -- like cross listed graduate undergraduate seminars that you took. Also good is if your profs writing letters have names that committees at least recognize. Finally, the statement of purpose should really be designed to make a potential advisor of yours, sitting on the committee, have as easy a time selling you to the others as possible. Political science, with its subfields, has a lot of horse trading in the admissions process. So make it easy on them: show fit, but also that you can work well with a few profs. Show preparation. Show you want to be a researcher and scholar, that this is your central goal, above all others.