The federal government has no constitutional authority to provide universal health care, per the 10th amendment which leaves an extremely narrow constraint of enumerated powers to the federal government and the rest left to the people and the states.
However, the feds already siphon about as much tax as the populace can bear just on accomplishing what it is allowed to do, so there is basically nothing left for the states to implement these kind of measures.
Yes, if the states were to take over many of these things, obviously federal taxes would need to dramatically decrease (luckily, the vast majority of federal spending is doing the things that I think states should do anyways, so you'd be simultaneously dramatically decreasing federal taxes and federal spending).
You couldn't just have the states take over these responsibilities and have nothing else change. My suggestion is in fact a pretty radical change in how the US federal government works. I'm not under any illusion that this is likely to happen. The ratchet of power unfortunately only goes in one direction.
However, the feds already siphon about as much tax as the populace can bear just on accomplishing what it is allowed to do, so there is basically nothing left for the states to implement these kind of measures.