This article ends with direct lines to call both DC and NYC offices of Senator Schumer and Senator Gillibrand. She also lists a sample script. Someone, if they have the resources and money (for paying for calls), could easily create an automated Twilio script to auto-dial this number with a pre-formatted script and insert some dynamic text for a name and phone number. You could then create a website for people to voice their concerns and auto-dial with an automated message on their behalf.
I think that's a pretty bad idea. The benefit of calling in person is that it shows that you really care enough to have an actual conversation with a person. If you're just getting 100 robo-calls it's going to seem like astro-turfing (which it kind of will be).
You can automate dialing through the menu so long as the tree is always the same. Twilio provides the ability to send key presses and is quite easy to use.
Thoughts?