Listen, the Presidents signature on a national abortion ban won’t be a Democrat. You’re extrapolating a political strategy when it’s simply: don’t sign a bill that makes menstrual tracking a responsibility of the United States Government.
Listen, when we look back at the achievements of presidents, we don't talk about the things they didn't do. We don't praise Ronald Reagan for _not_ signing a bill that reinstates slavery. We don't praise Carter for _not_ starting a war with Denmark. When I apply for a job, I don't tell my interviewer I won't shit on their desk, I tell them about the stuff I can do for their business. Saying you won't do something is not making an offer.