No current Padre was on the roster or made their Padre debut before that date.

If you go by amount of days (or games) where the player was on the 25 man roster or disabled list, then I think Heath Bell would be “longest tenured” (~4 1/2 seasons with the Padres starting in 4/3/2007).

If you count minor leagues then you are back to Stauffer again. Stauffer was drafted in June of 2003 and no one who is currently with the organization has a continuous tenure that goes beyond that date (I worded it that way because Bartlett was drafted in 2001 by the Padres, left via trade and returned).