This is a tricky one and I personally think there's no right or wrong, at least in most cases. It depends on the time frame the speaker has in mind most of the time.
However, I have some preferences. In everyday conversation, if I use the past tense said, I wouldn't quote the speech, instead I would change the speech tense to the past tense. For example,
Mary: What time will you be home?
Kate: I'll be home before dinner.
Jerry, guess what the first thing my mom asked when I told her I was going out with you? She asked what time I would be home. (I dont think 'said' fits well, 'ask' is better)
If I want to quote, either tense is OK with me though I'd prefer the present
I'm not a native. You might want to confirm with the natives