There is a 'cheap and dirty' walkaround ...
Enclose the package into a job, create a table TOTO with a trigger that fires on insert and that executes the job.
In your asp code, jus execute the query
INSERT INTO TOTO (filed1) values 'X'
Save your package as DTSRUN format and use dtsrun.exe utility.
(Do not forget to update dtsrun file on changes).