I'm currently working at my first internship where I negotiated a ridiculous lowball into a substantial lowball. I didn't have any other offers on the table and was worried that I wouldn't get anything, so I settled. I think my point is that it won't hurt to ask.
I later found out that I wouldn't be an employee, but a 1099 contractor responsible for all my taxes, making the rate even lower than I initially thought. Needless to say, they will have to more than double my hourly rate when summer comes for me to stay.