Stay in school. Sure, you will be racking up more debt, but as long as you are a full-time or more than half-time student, you do not have to start paying back your student loans.
Ask for forbearance. Forbearance is a temporary hold on loan payments. Think of it like an extended grace period. Each lender has criteria you must meet for this, so inquire with your personal lender.
Request a deferment. This is similar to a forbearance, but with a deferment you are usually still responsible for the interest in the grace period even if you aren't making payments.
Request a cancellation. There are certain instances (if you're teaching in low-income areas or in certain subjects) in which you may be eligible for a cancellation.