I'm using Verizon (since I'm using a Droid Maxx it's obvious) ...
For voicemail I dial ...
*86
... and it prompts for a password ...
1234
... and then a command to listen for new calls
1
If instead of ...
*86
... I use ...
*86,1234#1
... it will dial and enter the responses.
The next step is to use a Direct Dial widget and tell it to call ...
*86,1234#1
(replace 1234 with your password)
... Thom