A Supreme Court case is a different kind of beast. If it's a criminal case, it's not about the guilt or innocence of a victim. It's about whether all of the rules were followed. If they weren't, did it disadvantage the accused in such a manner that they didn't receive a fair trial?
If it's a civil case, it could be almost anything. But the attorney only spends 3 - 12 minutes presenting his case because the justices have been previously briefed on the case. The justices will rapid fire questions at the lawyer to find out as much as they can. They will interrupt the attorney as he answers. He either has his poop in a group or he looks stupid.
Bottom line: it's enough time. It often doesn't go that long.
If you get decent grades, do well on the LSAT and build a decent resume of other activities/experiences, you should not have a problem getting into a good law wschool just because you went to San Diego State.
(Also, law school often prefer if a person does something for a year or two after college, before entering law school -- if you do some interesting work in the meantime it will help a lot. But it isn't necessary.)