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I'd like to get some cash flow to help me with some of the debt, but I understand that my studies should 100% come before that. Are there any opportunities for law students the get the type of jobs on campus that you can just sit at a desk 95% of the time while studying and occasionally talk to someone if they come up with a question? The typical library desk type of job?

In undergrad these jobs primarily went to people from families with extremely low income (my family was far from wealthy but also didn't meet this criteria)

2L you can get that sort of job, although I've gathered they aren't easy to come by. Given the immense opportunities available during 1L assuming you are going to a decent school, I wouldn't be too concerned with work the first year. Look into it the summer after.