It seems agreed (for example in this questionthis question) that wish is usually** counterfactual; that is you wish that something actually the case were not.
I quit my job last month: I wish I hadn't.
I have to go to work tomorrow: I wish I didn't (because the emphatic form is I do have to).
But The office just called: I will have to go in tomorrow after all. I wish I...? Not didn't, because that means something else. Not won't; wish never takes will because in the case of a simple future you can just act differently, rather than wishing. Hadn't seems as if short for I wish I hadn't had to; again , different meaning. It looks simple, but I am at a loss: can anyone give a reasoned answer?
Edit: StoneyB has pointed out that will have to here may be equivalent to have to. I am not sure about that, but in any event there are other cases where the difference is clear. If Joe keeps coming in late, I shall have to fire him is obviously not I have to. If you then say I wish I..., then what next? In other words, how do you say in normal speech I wish that it were not the case that I may/shall have to fire him in the future?
** There are edge cases/other uses (according to taste), like I wish it would rain, I wish you'd keep quiet, and We wish you a Merry Christmas; subject to correction, I don't think any of them are relevant. And, if you have Aladdin's lamp, you can wish I had a million pounds and have it appear: whether that's counterfactual is rather too metaphysical for this site.