In case people are still stuck with this in July 2015...
I have an ex-Verizon Samsung Galaxy S3 that I have just got working with Consumer Cellular's help (Matt - you are a star!).
Two key steps above and beyond their advice on their FAQ page.
1 - This is a first generation LTE phone, so you must use the LTE Settings
2 - You must call up CC Technical Support and ask them to register the phone's IMEI number in their database. Even if all your settings are correct (as mine were) without this step (and turning Data off and on again) it will not work.
The IMEI is on the box, and also inside the phone under the battery.
You might get it to display like this at the 'phone' screen
Enter *#06# then press the call icon.
It didn't work for me, but I had the original box.
So, yes Virginia, the Samsung Galaxy S3 Will Work on Consumer Cellular.