What is chewing the bottom of my stem or is it stem rot? It is also happening to the cucumbers in the same bed and to one tomato plant on the opposite side of the garden.

I looked at photos, and thought maybe a cucumber beetle, but I don't have those in my garden. I have seen the following insects: aphids, black flies, red mites, leaf miners, leaf hopper, slugs, and a worm from the white moths that fly around.

http://s1049.photobucket.com/albums/s400/jdolan29/Plants/