Please no AI interpreting sentiment in emails, the error rate / hallucinations at that scale would be dangerous.
To be clear, not necessarily sentiment analysis of the email (the pre-LLM kind, like are they angry, aggressive, etc.); but sentiment tally about voting on the legislation, like a phone operator might do, which might only be identifying which bill/issue is being talked about, and whether "vote for" vs. "vote against".
The limitations of that is part of why I suggested that following up with review of the email by a human later, for nuance. The other part is so they know they're reaching a human at their representative's office, not just talking to a machine.
I don't know much about politics other than Sorkin-esque TV dramas, but the original Web page said that timely tallies could help a politician avoid being in the situation of having to walk back a stated position on something. So I'd guess that's one way a real-time tally could still be very valuable, and I think an LLM is up to the hard parts of it.