No state alone can, because it would have (or at least would fear) a large influx of people coming for the free healthcare. If enough states set up their own systems and make them interoperable, it might have some legs. I hear rumblings of this from time to time,

What I meant was a federally-mandated, state-implemented system. Federal law can define a minimum level of healthcare that every state is obligated to provide. States set up and administer their own systems, any way they want - single-payer, mandatory private insurance etc. Isn't that how Canada actually does it?

It handles the "US is too big" objection to universal healthcare that everyone loves to bring up, by moving the systems to a lower level.