There is a large difference between a manager orally mentioning a large bonus and HR/TPTB approving it. Did you get nothing in writing BEFORE you took the assignment? Did the manager copy anyone else on the original email about the promised bonus? Does he have the authority to grant bonuses and make pay decisions 100% by himself?
Who is telling you there is no money to pay it? The Manager?
I'd go above the manager's head to HR and ask them if they have any knowledge and let them know what was said in all conversations. But in the end, it might be a "you said/he said" situation and if the bonus was never approved, then you could argue he was acting on the company's behalf, but I doubt that will fly since you got not official documentation.

