Is your part time job related experience? If not I hope you don't plan on being out of your chosen profession too long. No one likes gaps in the resume. How will you explain your move to prospective employers? You can't say "they would not give me a raise during a time of recession and 10%+ unemployment so I told them to pound sand". It could be a hard conversation trying to not come off like an self-centered idiot. And most people try not to hire those. "I left to get my MBA" or whatever will sound as thin as it looks on paper. No one with a brain does that in this economy.
My experience is find a job while you look for a new one. And negotiations with the new employer is in your favor if you already have a job. Gives you bargaining strength.
The old saying "don't cut off your nose to spite your face" may apply here.
FWIW, once you get a raise based on a threat to jump, you often acquire a spiteful bulls-eye after that.