I think you can call customer service *611 on your phone or 1-800-922-0204 from another phone and your can get the password reset through there.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
I understand how important it is to access voicemails. Ann154 provided a great solution. You can also tap your My Verizon Mobile icon on your device, sing in with your credentials, tap device and change voicemail password. You can also reset your password by clicking here http://bit.ly/Iy7KAB and signing in with your My Verizon sign in information. If you are unable to reset your password please DM me with your name and mobile number so I may further assist you. Thank you.
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