You may be right although I have a hard time seeing that happening politically. IANAL, but the relevant case law seems to be Jacobson v Massachusetts (1905) upholding mandatory smallpox vaccinations which AFAIK has never been superseded. [1] That said, the US Supreme Court also upheld a Virginia law that authorized the involuntary sterilization of “feeble minded” persons in state institutions in 1927. It's hard to imagine similar laws passing muster today, probably for 14th Amendment reasons.

[1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1449224/