I think the private sector in the U.S. will have to be the ones to "lay down the law" and refuse service to anyone who chooses to be unvaccinated on principle (not those who can't get the vaccine due to age or compromised immune systems). I doubt the gov't wants to take on the role of mandating vaccines for all Americans--it's too politically risky and Democrats will worry they'll lose seats.
So instead, private parties need to be the ones to withhold services from the unvaccinated to protect their staff and customers. You can't enter this store, that restaurant, the office, or the hospital if you're unvaccinated without a justifiable medical reason. Your choice to refuse the vaccine means you're putting kids under 12, immunocompromised people, and other people who cannot get the vaccine at risk of death.
Frankly, I hate that our doctors and nurses are repeatedly exposed to COVID while treating the stubborn unvaccinated ones. But I doubt the medical community would ever refuse to treat unvaccinated patients. That just seems too harsh.