Doctors should be paid MORE. Yes I said it, more!
Whether they should make more or less isn't quite the issue at hand.
The real problem is that there's essentially no sane way to understand health care costs.
You say doctors work 12-hour days? Well, what if Medicare says some are billing for 26-hour days, and a hospital maybe says they're only spending 6 hours in surgery (that's a wild guess)? So, what's their hourly wage? How much of it goes to medicine, and how much of it is administrative busy-work? Can it be made more efficient? How?
If we haven't really got a clue how much doctors are being paid for the work they're actually doing (versus, say, the base costs needed to run their practices, hospitals, etc), then how in the hell can someone come up with a rational argument about whether or not they need to be paid more or less? And the same point applies to virtually every aspect of health care. Drugs, medical procedures, hospital costs versus billing, lab costs, technology costs, nursing staff, admin workers... you name it, and there's virtually no well-understood relationship between what it costs and how patients pay for it.
That's the real problem. Not how much doctors are paid, but the fact that health care is basically a big fucked up black box which nobody really understands how it works or how to make any part of it better.