Photo isn't totally clear. But if that cluster of small white things is what you consider eggs, not so.

Instead, cocoons of tiny, non-stinging wasps whose parent laid eggs in one of the caterpillars. (Oh yeah -- and the caterpillar is now dead.)

Thank you Jean for letting me know about the cocoons. I guess they are a good thing for the garden?

Anyone have any idea how I get rid of those yucky caterpillars before they kill my Zinnias all together? :(

All I could suggest is that you pick them off and squish them as you find them.

I am having trouble finding any info on species of caterpillars that attack Zinnias.

The one site that I did find that mentioned them simply repeated what I said. To hand-pick them.

While I don't have the cocoons, I do have these bothersome caterpillars. I pick them off every time I am in the garden, but there are always more. Often they leave what I assume are droppings (brown little dots the size of pepper) on the leaves and then the leaves are damaged. Yesterday the caterpillar was inside the bud of the flower eating out the insides.
Is there anything else you've done to get rid of these guys?

Have you tried BT. It kills only caterpillars and will not harm other insects or birds. It causes disease in the caterpillars and only the caterpillars.

There are several kinds, just make sure yours is just for caterpillars .

I got these grey catipillars on my zinnias. The one dude actually wiggle into the flower bud and ate it from inside. I've only seen a couple. At first I thought they didn't get watered but then noticed my seeds were eaten.
They move pretty fast for bugs.

Bacillus thuringiensis is not a magic elixar cure all but a specific toxin for leaf eating larva in the early stage of life. Spraying BtK beyond that early life stage is a waste of your money since it will not do what it is supposed to.
As with any insect control you need to look at what you have and determine if this insect really needs control, is the damage the insect doing too much to allow to continue?, or can this insect be allowed to continue to grow. Is this the larva of a butterfly that may be something desireable or is it a not desireable adult something? Are there predators around that will control these wee buggers, or have I sprayed something around that killed all of them off, or have they not arrived yet because there was not enough of this food source around?
As a rule, insects that eat seeds do not eat growing plants so you need to know which you have before any control measures are taken.

Very good comments, kimmsr. We (all) really need to be more thoughtful about when and why we use Bt-K

I had a great blue lobelia growing in front of my house- it bloomed this year and I saw a hummingbird in my yard for the first time ever. I was so excited. The blooms were beautiful, attracting bumblebees. The leaves didn't look so great, but it's been a bad year weather-wise and with pests too, so didn't know what it could be. Decided to let it go and enjoy this late-blooming plant. I noticed a brown spider had set up residence in the leaves, and thought great!!! He'll eat anything bad that might come this plants way. Well, it has been covered in green caterpillars, and the more I picked, the more there seemed to be. Poop everywhere.
No sprays. Hoping spider would eat cp's. Nope.
What "good guys" eat caterpillars?
Birds don't get that close to my house to be of help.