Medicare is not a blank check. It's a standard check (see sibling comment on fee schedules), and each check tends to actually be quite low of an amount.
The magnitude of "standard" and "low" are both demonstrated by the fact that when private insurers negotiate pricing contracts (basically, a one-off fee schedule) with hospital groups, they express prices in terms of "medicare multiples".
For example, the insurer will pay up to 13x of what Medicare pays for an fMRI administered under non-emergent circumstances with medically-justifiable cause. Pretty much every multiple is >1x, many are far more than 10x.
And medicare is arguably more expensive to provide, since the probability of confounding issues from disability or age is higher than in the general insured population.
Medicare is very consistent with paying, especially in comparison to private insurance, but the a la carte fees are quite "low" by relatively-freer-market definitions (I say relatively, because the reality is that private insurers negotiating with hospital groups is the antithesis of a free market, in most conceivable dimensions).
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The main reason medical groups lobby against "medicare for all" is that they will lose lucrative "20xM" payouts from private insurers, and it's difficult to see how their ballooning administrative costs can survive on such a lean diet.
Of course, this line of thinking is deliberately ignorant of the thought that medicare fee schedules can be renegotiated to reflect the population of patients "medicare for all" would incorporate. But nobody's interested in thinking two turns ahead, let alone advancing the game state, when their pockets are nicely-lined on turn zero.