I noticed that some of the winter squash leaves were wilting. To me, this is clearly an indication of the presence of a squash vine borer. I gave it a couple days, and it was only getting worse.
In addition to the wilted leaves, we also appeared to have small holes in the vines near the base, and "yellow brown excrement".
To find the worm, I pressed along the main vine starting at the base until I found a soft spot (which was on the bottom of the vine). I then used a knife to cut into this spot until I could spot a worm. This is the larger worm I dug out of the squash vine.