This is nothing but demagoguery. None of the major proponents of tariffs want to add them to the current tax rate. They want to replace the current oppressive tax system with tariffs. If we had tariffs instead of the income tax, imported goods made by prisoners in Red China would have no price advantage over domestic goods. Not paying income tax would more than offset the fact that the goods would cost more.
Tariffs also capture the underground economy.
Drug dealers and others would then pay these taxes too. Proponents of free trade claim we need to export goods to maintain our robust economy. This is nonsense. Japan is the world's greatest exporter, or was. Their economy is in the toilet, as are the economies of the other exporting nations in Asia.