Will they become high earners? The vast majority of taxes are paid by high earners and the wealthy, with those making under ~$43,600 a year—50% of Americans—paying just 3% of income taxes. (Source: https://www.heritage.org/taxes/commentary/1-chart-how-much-t...)
Existing Medicare funding comes (mostly) from payroll taxes, not income tax, and the two work very differently.
It'd be more informative to look at who's funding healthcare now, including the private portions. I doubt very much that the bottom 50% are only covering 3% of that.