Have you tried setting up the call forwarding on the Google Voice website? I don't use it, but I'm throwing out a suggestion.
So this worked for me. Log in to Google Voice on your desktop. Go to Settings, and below your Verizon cell phone number, click "Deactivate Google voicemail on this phone". It'll give you a strange number to type into your phone (mine was *73 I believe). Mine didn't work correctly the first time, I got a Verizon message so I restarted the phone and the second time it worked great. It'll make three little beeps then hang up. Now, on Google Voice on your desktop, click "Activate Google voicemail on this phone". It'll give you another number to enter and call. Do this and you should be good to go.
Your question gave me what I needed to configure my phone. Thanks!
My process was to follow the options on Google's Voice site. Afterward, messages would still get sent to my Verizon voicemail. I plugged in as stated above replacing with my 10-digit number (did not include a 1 before area code). Now this works as expected.
Google should walk you through the *71[your number] option.
S3 can do google voice just fine.
This worked perfectly for me, the first time around. I am so relieved to have my google voice on my new Samsung S3. Thank you so much for this information.