The consequences of a U.S. where its citizens weren't taxed in any fashion would be catastrophic.

Unable to provide basic services like road maintenance or electric grid, large swaths of the U.S. would become a third world country. Within weeks we'd probably split up into several countries, and California would go to war with Texas for control of water supply in the intermediary states.

Even assuming you allowed for enough taxation to provide basic social services like water, power, roads, schools, etc., the cessation of U.S. military presence would be far-reaching. I'm generally not a fan of imperialism of any sort, but withdrawal of U.S. military presence would instantly endanger Japan, Taiwan, and South Korea into being made victims of Chinese occupation or satellite control. The Pacific Ocean would essentially become a power vacuum with India an China vying to fill the void.

The E.U. is much stronger in recent years, but long-standing political traditions like Baltic/Swiss neutrality and the current state of (relative) European peace are largely founded on the assumption of American hegemony and NATO military alliances. Without American as the elephant-sized anchor to that military force, European powers like Germany, France and the U.K. would need a massive upscale of militarization at both the industrial and social level, or risk falling victim to Russia's designs of regional expansion.

Even ignoring international consequences, domestic oil prices would probably be in excess of $10.00/gallon, to say nothing of the dramatic plunge of value that America's fiat currency would endure.

tl ; dr I hate imperialism as much as the next guy but don't be so quick to start World War III by lobbying for elimination of all taxes in the U.S.