So, make income tax-free to a threshold of $30,000, with negative income tax to list incomes to that level for low-income earners. Everyone earning over $30,000 would get taxed more to pay for it, but if what you say is true, that both Republicans and Democrats want to live in a more equal society, they should support it. I bet you the left reinvent the poverty line to be $35K after this.
The down-side to this is that no-one would try to get off the minimum wage, since they would take home an after-tax $30K anyway, so it would screw up economic incentives for self-improvement. A working couple would have $60K to live on, well above the sufficiency line for raising a family so this would give a more equal society.
You would need to beef up border protection, though!