You cannot put a full block on text messages on the website. You'll need to call customer service and request it.
Thanks for your reply.
I did have all messages blocked until I had to call and unblock them in order to receive a single temp. Password text message from the Backup Assistant, in order to set up a new phone to use and backup the contacts.
The nice customer service lady said that I could re-block the text messages by using the VZ website. I will make another call to have the customer service people help with this.