Is this both an answer to "For how long" (Until tomorrow!) and also "See you tomorrow"?
No, they have different roots -- "завтра" (tomorrow) and "завтрак" (breakfast). But yes, they look very similar :)
Doesn't "до" always take the genitive?
Edit: I've seen "до скорого" and "до встречи" and "до свидания" which are all in the genitive case.
And it doesn't decline because certain time words function as adverbs, not nouns - вчера, сегодня, завтра never change.
That's actually what I started thinking when you said my guess was incorrect. Thank you!