Why can't I connect to my Solr server?
It turns out that if you use the IP of your host machine, if you're hosting Solr and the Site on the same box, you can't use the IP of the box to connect.  In my case, I was trying xx.xx.xx.xx:8983/solr/my_core which was failing.

After changing the address to http://127.0.0.1:8983/solr/my_core I am finally connected.