What are these caterpillars eating a potato plant?
I believe this is the middle instar of a Southern Armyworm (Spodoptera eridania) larvae. Or some closely related species in the Spodoptera genus (family Noctuidae).



 © 2016 Wings, Worms, &amp; Wonder  

The larvae undergo six instars as they grow to attain a length of about 35 mm.


You can see a series of life stage pictures from Mississippi State. 


Armyworms are so called because you typically find 100s at a time on a single leaf or plant. According to here:


  Armyworms strike in the blink of an eye, and there are so many in their army that you will be finding them for weeks after the primary attack.


Behavior: larvae are mostly active at night and hide on leaf undersides, in curled leaves, or in leaf litter during the day.


This University of Florida site claims


  Young larvae feed on under surface of leaflets leaving upper epidermis intact ("windowpaned"). Older larvae consume foliage and eat large holes in fruit. 



Range: native to the American tropics (occurs widely in Central and South America and the Caribbean). Also found in US (principally in the Southeast but extends West to Kansas and New Mexico). It also is reported from California.


Here's a map showing some confirmed sightings [source]:




Host Plants: 
This species has a very broad host range including important crops (including potatoes). 


I would be concerned for your nearby tomatoes, because thy too are a favorite food of these insects. 


See here for more information including management suggestions. 



Defecation vs. Eggs??

The picture in the question shows S. eridania's feces.


This Mississippi State site includes a great zoomed-in picture of S. eridania's feces:



 © Lee Ruth 
Note: caterpillars don't lay eggs. Only adult moths/butterflies lay eggs. 

Eggs: large masses of 100-200 eggs covered with moth body scales, found on underside of leaves, hatch in 3 days.



 © 2016 Wings, Worms, &amp; Wonder  

Here's a picture of inside the seed casing of closely related S. exigua [source]:




 © 2016 Wings, Worms, &amp; Wonder  



Finally, here's a picture of the nocturnal adult: