I just went outside. I should add that the adults have dark bodies that are shaped like the boxy part of a guitar case or cello and the biggest ones looked to be about a 1/2 inch long.

Squash bug eggs and squash bug nymphs.

Rhizo is right, and they will do damage. Eventually they will suck the life out of the plant. But they go much slower than SVB and are easier to remove--pick them off as often as you can and drop in a jar of soapy water, squash them as I often do. The nymphs are very delicate and smoosh easily. Also tear off the parts of leaves with the copper-colored eggs or you'll have dozens more squash bugs.

Thanks - I was afraid of something like this. There are tons of those critters on my plant. Also explains why I'm not getting any new fruit. I'm thinking burn pile and farmers market for the rest of the season. Is there time for a second planting maybe? Do these critters burrow into the ground and cause problems next year?

There's no time in your climate for a second round of zucchini as the days are getting shorter and shorter. You can help prevent next year's big outbreak by removing ALL the plant debris and any other hiding places where the adults might overwinter. Be sure to keep a close watch, next season, for the eggs so that you can put a damper on that generation, at least.

The adult squash beetles overwinter in "weedy" patches, under rocks, etc. more so then in squash vines in the garden. Mostly control, in the home garden, is to knock the wee buggers off the plants into a bucket of soapy water and encouraging the predators to be present which means not spraying a lot of persistant broad spectrum poisons around the garden.
Aside from the bucket of soapy water, Insecticidal Soaps, Neem Oil Sprays, Horticultural Oils and vegetable oils can provide some control, if used early enough in the life of the squash bugs.

Here is a link that might be useful: Control of squash pests