>"Would you favor or oppose the government's offering everyone a government administered health insurance plan like Medicare that would compete with private health insurance plans?".

Nobody wants to see anybody go without health care.
Nobody.

Is there any way to limit demand for health care?

A friend from India once remarked that where he came from, people would NOT spend the gigantic sums of money on end of life care like we do in the US. I asked him to explain. He said that nobody would take that much money away from their family, and that everybody dies anyhow.

Changing one third party payer for another won't fix our problem of unlimited demand.
Everybody wants to live forever, nobody wants to pay.

In the end, whether it is insurance or government, we end up paying for it anyhow.

The most basic problem is unlimited demand.

Our third party payer system has made it very easy to spend gigantic sums of money by removing the cost consequences from the spending decisions.

On a small scale, you see this exact problem with poor people and emergency room visits.
They take their kid to the emergency room for sniffles because they cannot afford a $50 office visit.
The emergency room is "Free" to them, but really costs like $3000 to the rest of us.

It would cost like $8.14 for that same kid to see a nurse practitioner in some kind of clinic.

No amount of cost-shuffling will fix stupid spending like this.

Walmart's $4 prescriptions need to be joined by $4 clinics to make a dent in this mountain of stupid spending.