It can mean a lot of different things, depending on where you put the stress:
THAT’S all I have to say = “That last thing I just said? That’s the key to what I mean.”
That’s ALL I have to say = “I’m done talking on this topic now, having probably said quite a lot.”
That’s all I have to say = “Someone else may have a different, much stupider, opinion.”
That’s all I HAVE to say = “I’m taking the Fifth.”
That’s all I have to SAY = “Time for action!”
Additionally, context can add still more nuance. English is not like a sequence of programming statements, each statement rarely has a complete and precise meaning all by its lonesome, it depends for its precise meaning on context and (in the case of the spoken language) intonation (sarcasm, fervor, doubt, questioning, assertive) and stress.