First of all, it is NOT a vaccine, it is a treatment. It does not prevent you from getting the virus, it simply tries to minimize the damage once you do get the virus. The reason they call it a vaccine is because other vaccines that prevent an illness are already mandated, so they muddy the waters to make it appear as if all is status quo with the jab.
Secondly, the mandate is NOT across the board. You don't see illegals pouring across the border by the millions being made to get the jab, and you don't see those on welfare being made to get the jab, all of which on average are not vaccinated. This is because they are the base of the democrat party and they are distrustful of the government even though they suck off it's teat to survive.
And lastly, is it Constitutional? I put this last because the Constitution always gets put last. Currently the mandates are being slapped down by the courts because they don't seem to be Constitutional, or do you even care? Does it even matter anymore?