An argument people like to make is "if you're smart enough to get into an ivy league school, then you're smart enough to specialize from your state school."
For some people (like Big Hoss or The Anhedonia) this is probably true, but I don't think that this statement applies to everyone because, as The Anhedonia said, there are tons of smart people at state schools that you will have to compete against. Are you confident you can be in the top 10-15% of your state school? Moreover, the lack of a true ranking allows individuals at Ivy league schools to focus on other things that boost their applications (studying for the CBSE/GRE, doing research, community service work etc). Personally, I cannot imagine having to juggle all the extra "stuff" that is required to specialize with maintaining a high class ranking. I truly respect those that manage to do this.
At the end of the day, it is up to you to decide if it's worth it.