My two cents:
 
Constructions like _ought to_, _dare to_,_supposed to, etc. work like
models, requiring the base or infinitive form of the next verb in
the string, and they have been classified as models by some descriptive
linguists, but I don't have the sources here with me.
 
Both _ought to_ and _supposed to_ are roughly synonymous
with the model _should_, and they occupy the model position perfectly
(coming before HAVE or BE or the main verb) so by analogy and on syntactic
grounds, if one wanted to classify _supposed to_ in traditional
grammar terms it would make sense to call it a (phrasal) modal auxiliary.
 
Notice that the _to_ can be dropped in the
negative: He ought not leave his wallet on the table.
 
 
 
--Bill Murdick