Needs to be repeated again & again:
"Governments have no money of their own, it's citizens' (past, present and future - mostly the latter these days) who provide the cash via taxes".
This changes nothing. If anything it is wise for goverments to pay for vaccine because that means that economy will no longer be stifled by lockdowns and that means more money in taxes.
In any cases many governments already said they will provide vaccine for free.