As mjp8 said, prestige only seems to factor into whether or not you can pull down a player.
I have never seen any evidence that roster makeup has any effect at all.
I wouldn't say that overall rating has any direct effect on the ability to pull down, but there is a general feel of a hierarchy, meaning that you likely won't be able to pull down the highest rated players and you will probably be able to get the guys toward the lower rankings, but I wouldn't say its tied directly to their rating.
The one thing I will add is in reference to the proximity. It seems like when a player is very close to your school (10-20 miles) it is much more likely that you will get the backup message and be able to pull them down than if that same recruit had been farther away.
Again, though, all of this just factors into whether you will get the backup message and then be able to pull them down. The only thing I have seen that affects the level of effort required to pull down is if another school is also putting in effort.