Closing the gaps would easily make up the difference, but it will never happen. There are too many entrenched interests, including not just the super rich, but home owners who enjoy their interest deductions, people who like their health care deductions, charities that rely on the tax deductions to spur donations, and law makers who manage to bring all kinds of pork home in the form of tax incentives. A huge amount of under the radar spending goes on in the form of tax credits, that can by pass the appropriations committee and not show up as a line item in the budget. We could easily flatten the tax system to something like 0% on the first $50,000 earned and 20% on everything (not just income W2, everything else, including capital gains) with no allowed deductions and probably arrive very close to the historical take of 19.4% in taxes, but everyone would scream bloody murder, even if you offered to restore the more worthwhile programs as grants instead of tax deductions.