Well, I'll give it a whirl. The only caterpillar in my Caterpillars of Eastern North America book that is listed as eating Verbena - and I'm assuming that's what it is given the flower in the background - is the Common Looper (Autographa precationis). I Googled their eggs and BugGuide shows has two pictures.
http://bugguide.net/node/view/...
http://bugguide.net/node/view/...
Doesn't look like an exact match to me, but of course, you're the one who can see them in real life so I'll let you be the judge. I can tell you it's probably not a butterfly because I don't know of any that use Verbena as a host plant. Good nectar plant, though! So you've either got moth eggs, or some other kind of bug. FYI, always tell us what plant their on because butterflies and moths are picky eaters. Butterflies more so than moths. I say put them in a container and raise them to find out! But that's just me. It says they also eat beans, cabbage, dandelion, sunflower, thistle, so there should be plenty of food for them.
Finally,
