Your statement is too general in nature. Who "pays" into the system varies wildly depending upon your income, who you work for (public sector versus private sector). union or nonunion, and your age.
You should drop the single payer argument and look at a more equitable way to finance health care first. No one talks about the inequities in how we finance health care, they only insist that "everyone have health insurance"...ie. if you aren't paying into the system we will force you to pay. Look around you, some pay nothing for heir benefit and many pay an extraordinary amount. That's where the inequity exists.
You've got the solution backwards.