I believe the most obvious translation of 일 할 날 would be "the day on which work will be done", or perhaps "the day on which I will work" if the 'I' is obvious from the context.
I am wondering if it is possible to say "the day until which work will be done" or "the day until which I will work" using that kind of adnominal construction (verb+ㄹ noun) without using a word explicitly meaning 'finish'?