Another person with this problem.
Bought my 38mm Apple Watch Nike with Cellular today from Apple. I had the no sim, no data plan issue when I first activated it. Called Verizon and it did work for about an hour. Then again, No sim, no data plan. Through the App I removed the device from my data plan, and re-activated it - viola it worked, for about another hour. Then again, no sim, no data plan. After doing this about five times I am now stuck in limbo, when the Watch app sends me to Verizon to login to my account, I now get the error: We are unable to activate your device at this time.
Hours and Hours on the phone with Verizon and I get three results: 1) They have no idea how the device requires your phone and the process to establish the cellular connection. 2) They don't understand that there is no removable sim in the device. 3) Hung up on, chats ended, no replies.
Basically I get no help. I will return the watch to Apple, thankfully they have a great return policy.