A lot of it can depend on the insurance you have. If you have medicare/medicaid than you are considered a schedule filler. Meaning you are assigned to the slots physicians use to fill up the schedule in between mainstreamed insured individuals. Each physician, depending on length of time they've been practicing have so many appointment slots set aside for "low-insured" individuals. Making some money is better than not making any money at all, that should be their real promo.
I had a friend who had heart replacement surgery. Because she had a bad heart and was on a waiting list she couldn't work so she had medicare. I guess you could say she was lucky because someone who knew her who was dying donated their heart to her. About a week after being home from the transplant she had an issue, she called to get in to her doctor and they scheduled her for two weeks out. She had to call her heart surgeon to intervene on her behalf to get in sooner. So I guess dying out on the floor with low grade insurance doesn't always get you in sooner unless you are lucky enough to have someone intervene.

Before Obama care people could get seen for routine stuff within a week or two now it's like two to four months depending on what the routine care is. Even with getting sick sometimes you get in faster using a walk in med clinic than being seen at a doctors office, of course the deductible is higher for those visits.