The official Verizon version of Jelly Bean with TouchWiz for the Samsung Galaxy S3 has leaked already and since been posted online at XDA with the version number I535VRBLI5. Some users did report issues with the file when it was first posted, but this seems to have been fixed and developers of ROMs are now baking it into their builds.
Official Verizon Samsung Galaxy S3 Jelly Bean update leaked
The first of these was JellyWiz, which is a complete stock ROM with a theme over it and a boot animation that is new. Other than this, everything is there that you could expect in Jelly bean. If you are fed up of waiting around for Android 4.1 on your Verizon Samsung Galaxy S3, you could flash the ROM if you bootloader is unlocked.
What this means for the rollout timeline for the official version of Jelly Bean is hard to tell. Verizon in the past have been slow when it comes to offering updates. Sprint on the other hand has already got the update out to their customers, so maybe Verizon will be next?
Hit the source link to get the Android Jelly Bean build for your Verizon Samsung Galaxy S3. But do take note that while this is official, it is still a Frankenstein ROM given it is the easiest way to deliver it to your device.