The expression 'any day now' can also be used in a bit of a sarcastic way when you are waiting on someone and want them to hurry up. Example: (Amy still can't decide what to wear, so Bob is worried they'll be late to the party) B: Any day now, Amy! (using an impatient tone of voice) A: Sorry, sorry. I'm almost done! In my experience, this use of 'any day now' is much more common than the one you have given (I got the quiz wrong, even though I am a native speaker lol), though it is still correct. To me, using 'any day now' to mean 'within the next few days' seems too formal for casual use, and even maybe a little antiquated. For example, if I were at work emailing a coworker or a client, I could say 'it will be ready any day now' (though I think older people are more likely to use this term). But if I were with friends I would say 'it'll be ready soon' or 'it'll be ready in the next few days'. This is my experience using American English. Perhaps other English dialects are different.

Hi Kate. Helpful expression! Honestly, I had to google it out. Thanks you for share it.