it'll be very difficult, but not impossible.
i'm an SGU grad who matched into rads at the brigham & women's hospital. i know of people from SGU who had interviews at various harvard programs as well. i'm not sure about stanford: from what i've heard it's harder to match on the west coast b/c people just don't know about st. george's students as much. but i think we're definitely gaining in reputation and if you have great board scores, great LOR's, apply early, and are assertive in calling/emailing during the whole ERAS/interview process, you may be surprised at what interviews are possible and how successful you can be.
also, do not think the previous match lists posted are totally complete. i know of several people who successfully matched in very competitive programs/specialties, and it's simply not on the school website.
hope that helps.