I knew that something fishy was going on, because the cucumbers had been looking a little wilted even though we've gotten plenty of rain. I inspected the vines yesterday evening and, sure enough, squash vine borers have found their way into my cucumber vines! This morning I did some major surgery on the plants: cutting into the spot where I saw the orange, sawdusty goo and extracting and smooshing the little vine borer. Then, I rinsed the wound with fresh water and mounded up soil over the cut.
I have no idea if I got all of the little boogers. I guess we'll see if the vines continue to wilt. A huge THANK YOU goes to Ginger for her explanation on how to get rid of these nasty little creatures.
As you can see from this photo, the top of the vines are still really healthy, so I have high hopes for them. I saw at least 4 baby cucumbers on the vines. I really don't want to give up any more vegetables to these awful parasites. I am fighting back hard this time!