It would be unenforcable:
Can the government or your employer make the COVID-19 vaccine compulsory?
www.today.com
However, they can make life difficult:
1.They can make it a requirement for passports
2. Most hospitals require workers to be vaccinated due to working conditions
3. Most schools require it
4. Companies can require it as part of their health & safety program, and can fire you if you don't comply (barring exceptions, which create further limitations for human interaction, wearing a mask, etc.)
5. Per the article, places like airlines, restaurants, stores, and stadiums can require it, within the anti-discrimination laws, which means they don't have to give you full service, but can offer something like curbside pickup
I mean, I'm definitely in the pro-vaccination camp, but I'm definitely not in the "be the first one to try a fast-track vaccine" camp. I was on heavy antibiotics as a kid due to invasive surgeries & suffered poor health for over 20 years as a result. Thanks to modern medicine & advancements in our knowledge, I can eat regular food again (yay) & not feel like crap all the time (double yay), but yeah, on a personal level, I'm not real excited about being given a vaccine where the long-term results aren't known.