Paying for the inefficiencies of private healthcare is about half of US govt spend on providing services (the only larger spend is transfer payments, and you can't pay $4b in annuities to senior citizens from a private insurance scheme that takes in significantly less than that. So probably you need to cut healthcare by more than a third...). I actually believe the US could stay safe on a much lower military budget (though god knows what a private donor funded military would look like) but that's not getting the overall budget cut by a third even if you zero it out.

Mathematically impossible to achieve the functions of the US government for a third of the cost without cutting healthcare spend. Which has been demonstrated to be entirely possible by other countries, but only by choosing to let more people die or, ironically, removing some of the dependence on inefficient private companies for provision...