Close, payroll taxes are social security and mediCARE (not mediCAID).
I just showed with a simple thought experiment that dropping the 47% number to 0% would have a negligible effect on the true problem of debts and deficits. Thus solving the 47% issue doesn't necessarily help.
Another way of doing that thought experiment would to be fully merge income tax, social security tax, and medicare all into one form and call them all income tax (heck for the self-employed it is already combined). Everyone would pay the exact same amount, the 47% number would plunge, and yet the bigger problem isn't solved. The deficit and debt would still be bad.
We need to fix over-spending and under-taxing. Doing that will lower the 47% number. That number is a symptom, not a cause. You are correct that our current path is not sustainable. But fixing symptoms doesn't make it sustainable.