jim,

NEVER eat any vegetables that an animal has bitten into. The risk of contracting a disease is not worth the risk.

There is another possibility that it could be rats. We have roof rats in our area, and my bait seems to keep them under control. Having said that, if I ever see teeth marks in a vegetable, I fling it as far away as possible. Don't just drop it near your plant thinking a returning animal will forget what's on your vines, and only bite into the one on the ground.

Raybo

Even though the size of the feces makes you think of rodents, it could be a hornworm. Generally they'll just eat the whole branch, leaves and all, though -- are you missing any leaves or branch-tips? Squirrels occasionally eat foliage too -- this spring I lost half the lowest branch of my Pink Berkeley Tie-Dye to what was probably a squirrel.

Take a look at this photo of hornworm droppings (enlarge the photo). Generally they're a darker color, but the shape is unusual and not rodent-like.
http://floridagardener.com/critters/Insect_Pests/HornWorm.htm

Hornworms will eat some of the tomaote also. I had quite a few tomaoes in my hoophouse that the hornworms also enjoyed. Their droppings are larger than you might think would come from a worm.