I would also add that although your chances of landing big-law at the top ranked schools are far better than at lower tiered schools, it is still a hustle to land the job.
I know several classmates at Columbia who struck out at the 2L EIP/On Campus Interview Program for summer associate positions. This is usually the only window of opportunity to get into big law, as interviews for 3Ls are far more limited.
Moreover, although I did not personally have such an experience, many with "heimishe" undergraduate degrees such as Talmudic Studies, Religious Studies etc. have told me that they found that their interview experience was unsuccessful.
That being said, looking for a job out of Columbia as a 3L seems to be a far more promising process than at other schools. I just want people to understand that you can not expect to walk into big law by default just by attending Columbia or similar schools.