This is why it is inadvisable to take out large amounts in private loans when the jobs you can/will get on the other side of the degree will not enable you to pay back the loan.
No federal programs or assistance for private loans. I would assume that with that amount in private loans, you have maxed out your federal loan eligibility. Federal loans are where you can get deferments, forbearances, all that stuff. With private loans, you are really at the mercy of your loan company. I don't know why you would end up with only private loans and no federal loans--to me, that's terrible planning somewhere.
If you haven't already, get whatever deferments and forbearances you can get on your federal loans. That will free up some cash in the short term for your private loans. Stay in touch with your private loan lender, and make whatever payments you can. Once you default with them, they are merciless, and will sue you and your cosigner. From experience, I can tell you that it gets very ugly.
The goal is to stay in their good graces just enough that they won't send you to collection, and won't go after you in a legal sense. I think that LynnInMN would tell you that the only way to do that is to make the full payment each month. My experience is that private loan companies will work with you to a certain extent, but at the point that you ignore them, they treat you like a deadbeat until the loan is paid off in its entirety. Which at 60k, will be years (and judgments and garnishments) later.
If you're not making payments on these private loans, then you are in the kind of trouble that doesn't go away (and your cosigner is too). As LynninMN said, you either need to get a "better" (read: higher paying job), or a second job. Complaining about minimum wage jobs is no good. Complaining about not being able to do public interest work is not good. When you talk to the loan company, you'll need everything you can get on your side--two jobs, 80 hours a week, and you still can't make the minimum. And they'll ask for documentation. And they still might go after you. They really only respond to extremes.