In the case of Clinton, I recall that the News Media waivered a bit, but few Democrat pols came out for Clinton’s resignation. After Hillary’s statement of support for Bill the subject switched from ‘Resignation’ to ‘impeachment’ and that clarified the stakes for the Democrat Party. They all lined up behind Bill.
This is different. The Democrats have had time to consider their position and Nancy Pelosi — the most powerful Democrat in Congress, if not in the entire Party — has said that Cuomo has to go. Plus you have the legal machinery of NY State under the AG / Gov-in Waiting. Cuomo is in a Box that Clinton was never in.