Nate:
Thanks. I actually thought of that too. Took me a few days to remember that I could use Firebug to view the full call and response.
The problem is actually in the documentation example, which I just copied to be consistent:
jQuery.post( cartAjaxUrl, { quantity: quantity, id: variantID } )
According to jQuery's documentation, jQuery.post defaults to trying to interpret the response (http://api.jquery.com/jQuery.post/), but it seems like jQuery wasn't determining the type properly.
When I changed my call to this:
jQuery.post( cartAjaxUrl, { quantity: quantity, id: variantID }, null,"json" )
No more errors.
Thanks for the help!