(Not no much an answer as a comment that won't fit in the box.) In any language a good portion of the meaning of a sentence is determined by context. So what you have is an example of a sentence in English which might have three different meanings in three different contexts. But there's no reason that there must then be three different German translations; ...
Ich fasse es nicht/ich glaube es nicht! (I can't believe it)
Das darf/kann ja wohl nicht wahr sein! (This may not /can not be true)
I guess, both exclamations are more typically used in case of a negative surprise.
As hinted by @phipsgabler, in case one a sentence more likely to be used is: Das ist unglaublich schön!
If you're specifically asking about the amount of minutes/hours/days/weeks/... you can use:
Wie viele Minuten/Stunden/Tage/Wochen sind es noch bis zum Muttertag?
If you want to make it less formal, you can also leave out the "sind es", making it
Wie viele Minuten/Stunden/Tage/Wochen noch bis zum Muttertag?
If you want to make it even less formal (...
There are different ways of saying this correctly.
"Wie viele Tage sind es noch bis zum Muttertag?"
"Wie viele Tage dauert es noch bis zum Muttertag?"
It is rather unusual to say:
"Wie viele Tage sind noch übrig bis zum Muttertag?" That would be the literal translation of your suggestion: "how many days are left until ...
This one was not mentioned yet, so this is another option. You could use "keine Wahl" which has a direct translation to "no choice", but I think here in Germany we would use that, maybe as a rhetorical question, but not only.
Jill: Habe ich eine Wahl? Ich liebe ihn über alles.
Jill: Ich habe keine Wahl. Ich liebe ihn über alles.
Joe: ... ...
I don't agree at all that there's no equivalent in German. On the contrary, it's a notion that Germans, too, are very familiar with and therefore express often. The magic word here is something that doesn't exist in the English language: Flavoring particles. Since they are missing in English, they have to be added in German which translations fail to do in ...
Not a question, but something you can use in these and some more situations is the phrase pronounced as isso, which comes from ist so "it is like this". (I think using the "correct" variant would sound awkward here. But it also makes this difficult to use in writing.)
I think there is no ideal translation in German, but some that come close:
Da kann man nichts machen.
Da bin ich machtlos.
would be fitting,
So ist das Leben. (That's life)
would work most of the times, too, or even the famous German word
could be appropriate.
In German one would say
Da kann man nichts machen.
or - in a more humorous way -
Kannst du machen nix. Musst du gucken zu.
(Note that the second one is grammatically wrong - that's the joke. Not everyone might know that saying but everybody will understand it.)