I also asked this question on Lang-8 and these are the (translated and paraphrased) answers I received. 当て here means the second and third definitions here. It is somewhat similar to 見込み or 見通し. One of the comments specifically wrote the following:
見込み ≒ prospect, likelihood, possibility
Therefore, the meaning would be "He ...
I believe they are just saying that they could have allocated the funds to go on a trip if they wanted but they couldn't come to a decision.
The third meaning from here: