Of all of the branches, I have heard the Air Force is the "easiest". No offense, but unless you have a degree with that 60K in loans and it is of use to the military, I would stay away from Army or Marines unless you are prepared for the likelyhood of ground combat.
Do you have Student Loans or just personal loans? If personal, then you may want to consider bankruptcy. That would be better than risking your life to pay back some bank. Student Loans are a different matter I think, but you may want to talk to a lawyer anyway to see what they say.
I personally wouldn't be reluctant to look at that option if I was in your situation. It's not just for banks, businesses, and celebrities. Normal people can file bankruptcy too to protect themselves.