This thread is quite old, but I wanted to share something I learned. If you plan to quit within 60 days of when your school insurance begins, you can retroactively elect COBRA when you need it.
Meaning, if you quit on July 1st and your school insurance starts on September 1st, then you don't have to pay for COBRA unless you need the insurance. If on 8/28/08, something happens and you need health insurance, you can enroll in COBRA as of the date that you left your job. You just have to pay for the 2 months worth of premiums. If you can avoid any accidents by 9/1, then you save 2 months worth on COBRA insurance.
If you need insurance for more than 60 days before your school insurance kicks in, then I would look into temporary health insurance. It's only about $80-$100 a month, and it's nowhere near as comprehensive as regular health insurance and has a fairly high deductible, but it's a good "major accident" coverage.