The answer is yes, it does matter. As a graduate of Notre Dame, I can tell you that I had many more entry level job opportunities than my friends from high school who went to state schools. It should also NOT be the only factor upon which an employer bases a decision of where to recruit. In the former case, you should also consider cost factors, alignment of specific degrees and majors to your career interests, and the effectiveness of the university career center.
Good employees come from all backgrounds.
So if going to a name school is your tiebreaker, it is a valid tiebreaker. However, you need to take into account the myriad of other factors. I hope I've helped rather than hindered your decision process. Best of luck to you. Let me know how things go for you.