There is problems though, I'll admit that. Waiting times and shortage of doctors is a big one, but that is also due to how insurance companies tend to put more money in doctor's pockets to diagnose a certain way in USA than in Canada because they have more control there. I've read about doctors who were originally from Canada that moved back or American doctors who moved here because of how inconsistent it was to deal with patients and how hard it was to do any good with insurance companies the way they are.
Personally, I've never had a problem. I've had to go to the hospital twice in my life, both for non-life threatening injuries (broken arm, leg) and I waited 45 minutes the first time and 2 hours for the second time. I'm sure its not that much different in any standard American hospital. I also have a regular doctor I go see and it was not hard to get, but I do live in a city. Walk-In clinics are almost just as good, I've had to go to one a couple times and waited maybe an hour at most.
In any case, I'd rather wait an extra hour or 2 and not have to pay for it then only wait 45 mins and have a 5000 dollar bill at the end.