Can I get short term disability without short term disability insurance?

First off.. when did you get your notice of unemployment ineligibility? If its still within the appeal period, i would appeal. http://unemploymentguru.com/new-jersey-appeal-process.html click on that link for the appeal process in NJ. Most claimants don't know that they have the right to appeal the initial determination. I've been unemployment advocate for a long time and also feel bad that claimants aren't ever as prepared as the employer.

No. You'll just be not working. If you resigned then it would be in writing. Argue the unemployment. I have a family member just fight that as they said it was 'for cause' and he won. And, it was a religious organization no less....real nice. You just go to arbitration and it doesn't cost anything. They'll hear both sides and make a judgement.