As I already said in the other topic: This MUST be a user-configurable option.
The new message system already uses "past 24 hours" as its definition of "today". The choice should be between that and this proposal.
You can already put "1" in the "messages from the last X days", now that I can think of it. Which then searches by the time since you click the send button, and not turns, right?
To think of it, may as well default "today" to last two turns, then, since the last 24 hours can be achieved through other means.