Weird - am I about the only one who realizes that not only are you quitting on the company, but you're also quitting on your coworkers? Unless there's zero mobility from one company to another company in your field - which you've proven isn't true - you never know who might be your potential boss 10 years down the road. If it's someone who remembers, "I remember her, she's the one who waited until Friday to tell us she quit" - it could have repercussions.
How about this: talk to your boss - communicate. "I have an opportunity... full time, with benefits... need benefits, especially insurance... can work until the end of the week here if you need me to, but would like to start the new job ASAP to get those benefits in place, plus start earning more money so I can cover my living expenses plus student loans." The boss might say, "if you want this to be your last day, that's fine." Or, the boss might say, "yeah, we need you until the end of the week." Don't give in to a "we need you to give two weeks" demand.