How's that likely to happen, when all people will see is taxes and no benefits?
Most people aren't on Medicare, Medicaid, or Social Security. Most people aren't on welfare or WIC. Still: try getting rid of any of those programs.
I have a friend whose child went onto Medicaid & Social Security disability (I think those are the right ones - whichever ones are for disabled adults) the day she turned 18. The girl is disabled, no doubt. But my friend talks endlessly about how she hates the idea of "government health care" and doesn't see the irony.
Give it a year or two, and no one else will, either.