Universal healthcare is not something that can work, as i have witnessed firsthand, growing up in Russia. While on paper, everyone had 'coverage,' the truth was that you had to jump through hoops and know people in order to actually get anything remotely resembling treatment for whatever ailed you. IIRC, even getting basic treatment (e.g., seeing a nurse) was a hassle, since there was one assigned to a specific area, for which she was responsible. I think they made housecalls. But unless you knew her personally or could give her a 'good' reason to come visit you, let's just say you may have had to wait for help for quite some time. Same applied when going to the hospitals; people would get admitted but only get worse since the staff did not exactly have the incentive to treat them.
So, all in all, universal anything (as in gov't programs) IMO is not going to work. When the benefits of any government-administered program are supposed to benefit the masses, with only a fraction of the population paying for the program, the quality of provided product will decline with time, as well as the amount of those who receive any resemblance of a quality product. There will always be those who get a better product under any program (probably because they are willing to work for it), while those who cannot afford it, will at best be slightly better off than they were before that program being instituted.