Yesterday Gary Becker proposed switching to a consumption tax, one which could be made progressive. Since a progressive tax has higher rates for higher incomes, it's a bit hard to think how this is possible. If I buy milk, how will the government (or the store for that matter) know how much I make?
A progressive sales tax is progressive in an indirect way. We know that wealthy people tend to buy certain goods (superior good), middle-class people buy certain goods (normal goods), and poor people buy certain goods (inferior goods). Note in this case, an inferior good is not a good of poor quality. It's just one where people buy more of it when their income falls. College is an example (few wealthy people go to college).
Under progressive consumption taxes, restaurant food should be at a high tax rate, fast food at a moderate level, and little-to-no tax on food bought in a grocery store. Concerts should have a high tax and board games a low rate. The internet should be moderately taxed or not taxed at all.
The only issue with this kind of tax is its implementation. As you can guess, cataloging all these different goods would be incredibly time consuming. It's tempting to divide goods into large segments but selecting something as broad as "cars" becomes problematic. There are luxury cars and basic cars. In some places (e.g. NYC), many low income people don't have cars since public transportation is sufficient to meet their needs. In rural areas or in western states, this is less the case. It gets even more complicated considering some low income people need their car to operate a small business, regardless where they live.
Of course, we will have to accept some imperfections in a progressive consumption tax system. Imperfections are inevitable. But it's worth thinking about how it might work in practice.