The Democrat decided to reject the measure because it applies only to the biggest and most expensive AI models and doesn’t take into account whether they are deployed in high-risk situations, he said in his veto message.
Smaller models sometimes handle critical decision-making involving sensitive data, such as electrical grids and medical records, while bigger models at times handle low-risk activities such as customer service.
I don't think this is the type of thing that armchair theorizing is good for. If you believe it's good to experiment with signature collection and talking to passerby about AI and/or getting more people on PauseAI mailing lists, I encourage you to do so and report back.