The girl from the rich family writes to the guy who she has now developed feelings for:
I've seen 応えたい with words like 期待、要求 or 想い, but with 日々? Does she implicitly mean "the happiness I have felt during the days I have spent with you"? And that she wants to give the same happiness to him? Or is it more along the lines of "I came to think that I want to make the time we spend together a happy one"?
This is very difficult. The author use "応える" in somewhat his original way.We don't say 日々に応える. I read the original text. In my opinion, あなたと一緒に過ごせる日々を私が可能な限り応えたいと思えるようになりました。means あなたと一緒に過ごすかけがえのない日々を私に可能な限り大切にして過ごしたいと思えるようになりました。.If the guy you say also have the feeling for her, this "応える" may equals to "恋心に応える".