In theory, Medicare should pay for this sort of care. In practice, it is hard to see how Medicare could be expanded to pay for long term care in the current economic and political climate.
With Americans living so much longer lives than they once did, LTC becomes something that many people will need at some point in their lives. It is also fairly expensive, making it difficult for people to pay for on their own. For these reasons, it would be good for Medicare to cover it.
But Medicare is already facing a huge crisis in financial terms. It takes in much less in revenues than it pays out. It is unlikely that people will accept having their taxes raised very much so it will be very difficult to add expensive new benefits to the program.