Proposals for a public option, capped hospital payment rates, or Medicare for All would save consumers and the federal government money, in part by reducing hospital payments. Such reductions could have a substantial impact on hospitals in the US and would therefore need to be phased in to prevent disruptions to the health care system. In this paper, we examine the phase-in period needed to reduce private insurance hospital fees to 100 percent or 125 percent of Medicare hospital fees under three scenarios. The first scenario would freeze private insurance hospital fees while allowing Medicare fees to grow at projected rates. The second would reduce private insurance hospital fees by two percent per year. The third would reduce private insurance hospital fees as needed to complete phase-in within 10 years. The paper illustrates the difficulty in achieving Medicare or near-Medicare hospital fees in private insurance without a significant phase-in period to prevent adverse effects on the hospital system.