L-F also reminds us that in North American speech, have got to is most often reduced to gotta, and is most often used to express affect on the part of the speaker. [I must admit I don't really quite understand what that means.

She also points to a 1983 unpublished master's thesis by a S. L. Melrose at UCLA suggesting that "most native American speakers reserve the use of must for expressing inference (present and past):
You must have the wrong number!
John must have been joking when he said that." (p.150)
Melrose, in her study, also concluded that "have to is used in speech to express both external and internal social necessity" (p.150). This tends to contradict my view of the matter, as I believe use of have to expresses an external necessity, if what is meant by that is that the speaker conceives, at the moment of speaking, that the source of necessity resides outside his control. In opposition, in my view, must is selected by the speaker who believes, momentarily, that he is himself the source of social necessity.
But who cares!
Larry Latham
*The Grammar Book, Marianne Celce-Murcia and Diane Larson-Freeman, 2nd Ed., 1999, New York, Heinle & Heinle.