How many Rabbit Hutches can take on a Spider Den?

I don't know if my answer will help you but every Spider Den contains a finite number of spiders, so, the farm won't last really much :

Tier 1: 3 Spiders
Tier 2: 6 Spiders(1 will be a Warrior)
Tier 3: 9 Spiders(3 will be Warriors)

Source: Don't Starve Wiki / Spider Den

Sorry if I missunderstood your question and Good Luck playing!

EDIT 1: I made some calculations and about 3-4 Hutches should be enough to finish a Tier 3 Spider Den, maybe even 2. I calculated all this by scaling the health and damage of a bunnyman with the health and damage of a spider and then multiplied it with the max number of spiders that can be spawned and added bunnymen to this. I think I just got it right, good luck with all that and all I can recommend is experiment it in-game.

EDIT 2: If your sanity is low, I can guarantee 2 Hutches are enough, because of the damage multiplier of the bunnyman, so 1 bunnyman can finish a spider in 2 hits and a spider can finish a bunnyman in 10 hits. (only if your sanity is low and the dmg of bunnymen is 60!)