I am assuming in this single payer scenario that the money people pay to private insurance would be funneled to medicare. My work sponsored family plan is over $500.00/month. I would assume medicare payroll taxes would go up that much. I hope not more than that.
I always assumed that this would be farmed out to companies that already have Medicare HMO programs, which are all the big carriers.
I think the dirty little secret is that health insurers could potentially love this. They became plan administrators for the government at a fixed price, and then pay at CMS rates.