Is it 1 million or 3 million? Because not knowing the difference of 2 million people isn’t a sound, quantitative basis for making policy. What if the impact on jobs was 0? Or -1m, i.e. a million jobs added?
Nobody probably knows how many private providers would remain, and how much they would shrink (yes, single-payer countries usually still have private insurance providers, clinics, hospitals, etc). Pretending you can know a precise answer is worse than admitting you just know there would be a negative effect in that job market.