Start by taking the rest of the day off. Go home sick if you have to and regroup. Don't quit while you are angry/upset. If you still feel like you want to leave write a resignation letter tonight and do it in the morning or after a few days when you have gathered your personal effects/data.

Quitting whiteout having something lined up OR not having enough cash in the bank is always a last resort but sometime if things are that unbearable it has to be done.

Also, this is not the last time you will be rejected for something you really really want start preparing yourself for that ahead of time.