For some time now some on the political right have been complaining that under current law nearly half of the U.S. population pay no federal income tax. But this assertion is at best very misleading.
Of course, as you already know, hardly anybody in the U.S. escapes paying taxes of various types even if they don't owe federal income tax. But what's less obvious is that the great majority of Americans in fact do pay federal income tax during a substantial part of their lives, even if during their youth or their retirement years they don't make enough to owe any.
A concise report from The Hamilton Project published in April shows that for Americans 40 to 60 years of age, between 70% and 80% of them pay federal income tax.
(The figure is somewhat lower at the moment because of the Great Recession, but that's obviously an anomalous situation.)
Furthermore, if you include federal payroll taxes, which of course are taxes on income even though they're distinct from what's labeled "income tax," then about 80% (or more) of Americans pay taxes on income between ages 20 and 60. Only the poorest 20% or so manage to avoid those taxes (and for course virtually all of them they pay other federal, state, and local taxes).
Incidentally, it might be worth noting that when originally introduced, first during the Civil War and again in the early 20th century, the federal income tax applied only to a very small fraction of Americans with very high income. That hardly meant that the rest of Americans were irresponsible layabouts living on the dole, contrary to what Mitt Romney suggested in the video that emerged last week.