Will anything attack my Pumpkins if I remove the netting now?

Now that I've found out that I have Pumpkin plants (and not courgettes!) I was looking to remove the netting that I placed around the plants.

For background info my plot is fairly unsecured and I've had problems with rabbits and mice, so up till now I've put green netting around each patch/trench which seems to have done the trick.

However now the netting is confining the plants and I was thinking of removing all of it, so is anything likely to eat my forming pumpkins? Or am I being paranoid? 

To my way of thinking, if it's worked so far then leave the netting on.  I know its a pain to weed round, especially pumps, but bunnies and mice aren't to be taken lightly (specially not bunnies).

It'd be a shame to lose your plant after all this time and  care, so net the main section at least