I've time for today

Yes- I've is a contraction that means, 'I have' so she's saying, 'That's all I have time for today' .
But I don't think it means this: "Well, that's all time for me today."? (although I don't really understand what that means, so that why I've written that I don't THINK it means that- in other words, I don't know for sure, as I don't really understand that phrase myself).

What about reading: - That's all I've time for, today?

Common- but old- fashioned - colloquialism:

Well, that's all I've time for today."

Well, that's all I've spent for today.

Well, that's all I've talked for today.

Means: that's my limit; that's all I have for that.

Well, that's all I've time for today. = Well, that's all I've got time for today.