I think it depends on the context and dialect.
For the first example, If you have a small sentence with a clear context, the message is clear as well!
This is a day's work = This is a one-day work (where one-day would serve as an adjective).
However, if you dig in further, what Jasper says seems to be correct. I searched for the term on COCA where ...one day work.. in sentences mean some day it'll work.
The list of examples prove it:
We picture him a biologist, an entomologist, someone who will one day work at a university.
He became a specialist on the dive team because he figures he can one day work as a commercial underwater welder.
Alysha even made up her mind that just like Dion, she would one day work with famed record producer-songwriter David Foster.
BUT, as I said, that's for the first example of yours.
While Tetsjin says in the comment that in BrE, it does not sound grammatical and COCA backs Jasper's view on this, Indian English takes some liberty.
In InE, such usage is fine. We often say, "I got a two-day notice from her lawyer" or similar example. But I'd certainly use a hyphen there. So the comments teach us that if I'm writing for the American or a British audience, I'd certainly use 'a day's work' and other all first examples over the second ones.
[Since native speakers feel it down or ungrammatical, it is advisable for non native speakers like me to avoid it though it's too common in InE].