The data is clear
53.5% pay federal income tax and payroll tax
28.5% pay federal payroll tax
Of the remaining 18% of the population, the majority of them (10%) are retired people no longer earning income. Only the remaining 8% pay no federal taxes (and that includes students in college who are not earning much income as well as the poor. The unemployed members of the population do pay federal taxes, as unemployment benefits are taxed (definitely payroll taxes, as for income taxes it depends on how much they make).
The Republican Party draws its strongest level of support from retirees, who have the highest percentage of any age group not paying income taxes