There's lots of ways to fund the government without income tax. Right now there's capital gains, corporate and payroll taxes in addition to all the excise taxes and fees on things like gasoline and telephones.
But if we wanted to go further and get rid of capital gains and payroll taxes there's still the corporate tax which is constitutional. But there are even more constitutional ways to fund a lean efficient federal government.
We could tax bad things like pollution (not CO2, but real pollution), cigarettes, etc. This would encourage companies to earn more income and innovate to generate less pollution and harmful products. We would also have the excise tax on gas to pay for the highways.
If that isn't enough, a "state-rate" tax can be imposed proportionally amongst the states to fund deficit spending in emergencies (national defense for instance). So a state with 10% of the population would be responsible to pay 10% of it's revenue to the federal government. This is good because it encourages politicians to desire less spending and not more, except in emergencies.
There would be all this revenue but more importantly, the spending would be reduced to constitutional levels without all the federal departments and bureaucracies. And keep in mind the states could still impose whatever taxes they like. But because the states are closer to the people, it's much easier to make them change their taxes if the citizens don't like it.