I don’t want to get into an argument, but I don’t think you quite understand the issue at hand.
The government is the only payer. That’s what “single payer” means. Hospitals don’t “lose money” anymore than a public school does. It’s all government. The only way to pay doctors more is for the government to get more money. They only way to do that is to raise taxes... or to take the money from other government institutions. Look at the numbers for how much a bare-bones single-payer system would raise taxes already. Then think about the American political scene. We can’t even maintain SOCIAL SECURITY (which by definition pays for itself) in this country without politicians dipping into it.
I absolutely understand that the government is the single payer, that's why the system would be cheaper, there's no profit that needs to be made by the money movers. Furthermore, when I say "lose money", I'm talking about opportunity cost. Let's say a hospital sees X patients and employs Y doctors for Z income. All of a sudden, everyone has health insurance, and now there are 2X patients that can be seen. Well, with only Y doctors, who can only work so much or want to work so much, then can only see a certain number of patients. This would incentivize hospitals, etc. to hire more physicians because they know that without more physicians they are "losing" valuable dollars that could be gotten from that sweet single payer for helping these newly-insured patients.
And no, there are different ways to pay doctors more. When you consider that physicians are becoming employees more and more, thanks to this ridiculously confusing multi-insurance system we have, their salaries are at the whims of administrators. So, if the administrators chose to increase physician salaries, they would go up, because it's not like physicians right now are getting all the cash they bring in. What would make administrators raise salaries or provide more jobs? Well, maybe if they knew they needed more physicians to cash in on these new patients, more jobs opened up, and physicians could better negotiate thanks to their other offers.
Lastly, if you're arguing that a government-controlled system is a poor idea because "take a look at what they've done to social security", I would say that you would need to vote against the people who want to destroy social security, and would likely want to destroy a government-ran system, in the effort to prove that "government things don't work" and therefore need to be privatized so their buddies can make money, just as you're essentially saying here.
Lastly, about taxes, sure taxes go up, but the overwhelming majority of people save money because they no longer have premiums, copays, coinsurance, etc. So essentially the bottom 98% of people would save money, and when you get to the upper echelons more overall is paid, but its around the 5-10k range I believe.