Why is the particle で used? With time expressions the で particle expresses time limit. So it's weird to see the で with 明日. 明日もいいよ seems better(?). でも here can be the "even though/even/but" meaning. But も sounds better(?).
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One way to think of it, which I found in the Dictionary of Basic Japanese Grammar, is:
＝ verb meaning “to be” ＋ particle meaning “even”*
〜でもいい is the です/だ version of the grammatical pattern 〜てもいい, which we use when asking for permission to do things. By putting the verb です/だ in its て-form, we can then ask if the thing itself (a noun) is permissible.
I recently wrote a blog post on this actually! Rescheduling appointments without sounding like a jerk… 〜でも…?
I feel that, this use case of でも is an abbreviated form of であっても。
(Note, I recognize there exist those uses of でも which do not fall into this category.)
So in here, もし時間がないなら、明日でもいいよ。 is an abbreviated (or colloquial) form of もし時間がないなら、明日であってもいいよ。 which translates to:
If no time, it is OK to be tomorrow.
Or something like that.
Please note that this is based on my recognition so when speaking in terms of Japanese strict grammar, it may not be precise.