I'm not sure. I have not heard of a push to make vaccines mandatory in a general sense. Governor McMaster is a very conservative Republican who said it should be left up to the businesses (that if they want vaccines as a condition of employment that is their business).The comment was specifically ragging on “Anti-Anti-Vaxxers.” Being vaxxed is not the same thing.
Any Reps pushing for mandates to be vaxxed or else? The Dem admin is pushing it hard. It's very political.
Pelosi could probably shut the admin up by actually contending with them, for example, by calling it unconstitutional...and racist.