I think you'll find that wait times and the need to carry private insurance in single-payer healthcare nations are mostly confined to elective procedures, not actual health-threatening conditions.
Our federal and state governments already pay half of all healthcare billing via Medicare, Medicaid, VA, etc. We also, in total, pay twice as much per capita for healthcare while getting poorer outcomes for that. Simple math would show us that adopting a single-payer system would cost no more than we now pay, without premiums, co-pays, deductibles, or any out-of-pocket expense, and we could police the industry to achieve better outcomes.
This would also free up about a million workers presently employed in totally non-productive capacity, either in insurance directly or submitting claims for healthcare providers to the myriad of insurers, each with multiple plans and differing coverage.
This would constitute a serious deflationary event, which we could use right now. Any politician who would claim we need to "pay for" a deflationary policy isn't bright enough to have an opinion, much less decide our economic policies for us.