When the POTUS wants hospitals to be built, he or she could do so through an executive order, likely through the Department of Health and Human Services. There is just a slight problem: Building hospitals takes money, and it is unlikely that the DoHHS budget has enough non-earmarked funds which can be diverted to this project.
Whenever the US government needs money, they need to ask Congress and Senate to change the budget. So the government would propose a bill which earmarks funds for this project, either by diverting them from other government programs, by raising more taxes or by making more debt.
Now let's say the bill get a majority in both houses, but some local politicians don't want the US government to build a hospital in their city. Maybe they don't want to drive the local for-profit hospitals out of business. Maybe they oppose public health care for ideological reasons. What could they do?
They could check if there is anything about the budget bill or the executive order which violates the constitution in some way. Then they could try to get the US Supreme Court to shoot it down. If that doesn't work, even the federal government needs a building permit when they want to build something, so they could just refuse to give one. Or they could make local laws and regulations on the state- or county level which apply to hospitals and make it impossible or infeasible for the federal government to operate a hospital in their municipality.