Depends. Is one of your professors who is writing a letter of recommendation an MIT* grad or worked for a professor there as a postdoc? Or have one of his or her long-term collaborators at MIT*? Do you have solid experience as an undergraduate researcher to go with your GPA, GRE scores, and appropriate coursework? Is one of your letter writers a big shot in his or her field, with Gordon Conference chairmanships and significant editorial prestige under their belt, along with invited reviews to PNAS (or other suitable journal) to tell the wider scientific audience about their work?
Speaking as a state school grad (Penn State here), pretty much everyone who I knew who was planning on attending grad school for the natural sciences or med school got into a more than suitable program. (Those who went the MD/PhD route probably had a little rougher, but that is expected, to be honest.) I have friends and old acquaintances at Harvard, MIT, Columbia, Yale, Stanford, Berkeley, Caltech, Princeton, UIUC, Chicago, and others.
Also, you cannot discount the capricious nature of admissions committees. I met someone on the recruiting tour that I did the March before I started school who was pretty much identical to me numbers & experience-wise, slightly better ranked school according to U.S. Snooze and World Report, but got into school X and got dinged from school Y. I on the other hand got dinged from school X but got into school Y. Who the heck knows why, maybe the tides were coming in when they were making the decisions for him but going out for me, and that affected the committees differently.
*: Or other suitable dream school.