Here's a nice "data and fact based analysis" if you would like to leave the hyperbole of Stossel, the insurance industry, and the Rightard Fear machine and actually venture out into the reality based world.
In fact, aside from Canada, we were least likely to be able to get an appointment on the same day, and most places could provide access to a doctor in an ER faster than in the US. So is access really worse in universal systems? It would appear that in most universal systems, doctors in clinics and the ER are more available than in the US.
Of course, if you find ideological dogma more alluring than the truth, nobody can help you.