There are a couple factors that will limit either San Diego or Oakland’s ability to trade down for a huge bevy of draft picks—
First is that after the Cardinals at #3, the first team you get to that has a glaring QB need is Pittsburgh at #11. Moving up from 11 is awfully tough if you don’t have two first rounders. After that, you have to go to Tampa at 15 and Miami at 20 to find teams that might want a first round QB. Neither have the draft pick ammo to make that huge move.
Also, if you are SD or Oak, do you really want to trade out of super blue chip area?
Last, Drew Henson continues to lurk. His rights can probably be acquired for a single first round pick, or more likely, a second and another mid rounder. This will also tend to take a little steam out of the trade up market.