Vaccines are already required to attend schools, daycare, college, to immigrate to the US, for many existing federal jobs, to join the military, most jobs in the medical field. These requirements have existed for 20+ years, society has tolerated these costs and benefited greatly.
I could see OSHA having a vaccine mandate that covers TDAP, MMR, polio and Hep B similar to the proposed covid mandate for large employers. But all of these are required to attend school and in other situations, so it isn't needed.
>What about drinking and smoking?
Drunk driving is a crime. Society doesn't tolerate it. We generally limit second hand smoke, banning smoking in restaurants and many other indoor buildings. Requiring vaccination to prevent the spread of infectious disease is analogous.