Mitt Romney’s sneer at Americans who don’t pay federal income taxes is dangerously wrong, based on a fallacy that widens an ugly divide in the country he wants to lead. He should stop embracing this mistake.

In videotaped remarks released Monday by the liberal web site Mother Jones, Romney told donors at a Florida fundraiser in May that he had already written off “47 percent of the people” who in his opinion will vote for Obama “no matter what.” Fair enough – political experts agree that each candidate has locked up about that much of the electorate. The fight, experts say, is for a small number of independent voters.

But then Romney described Obama’s 47 percent. They are, he said, people who “pay no income tax” and are “dependent upon government.” They are people “who believe that they are victims, who believe the government has a responsibility to care for them.” To sum it up: “My job is not to worry about these people. I’ll never convince them they should take personal responsibility and care for their lives.”

The comments have since been cheered by conservatives, who see the 47 percent figure as irrefutable evidence that too many Americans want handouts from a government happy to provide them. A closer look, for those willing to take it, tells a vastly different story.

According to the Tax Policy Center, more than 53 percent of American households paid federal income taxes in 2011. The next largest percentage of households, 28.3 percent, paid no federal income tax but did pay the payroll taxes for Social Security and Medicare. That’s more than half of the 47 percent Romney cites.

The reason those Americans are paying payroll taxes? They have jobs. They’re working to pay bills and feed families and move up to a better job. They do not have their palms facing up, ready for the next government handout.

The reason this 28 percent pays no income taxes? They qualify for tax deductions and exemptions because they make little money and have children. Many of those deductions and exemptions come thanks to the tax cuts championed by President George W. Bush last decade. Romney, by the way, wants to extend those tax benefits.

An additional 10.3 percent of U.S. households pay no federal income taxes because they’re elderly and retired. Many in this group aren’t taxed on their Social Security benefits, which they paid for from wages they earned by years of working. What’s left is 6.9 percent of households, non-elderly and not working, that don’t pay income or payroll taxes. While some in that group may be perfectly happy with joblessness, even the least charitable among us can acknowledge that some of the 6.9 percent includes people trying to find work, people wanting a better life.

It’s possible Romney doesn’t know these figures. Or perhaps he ignored them at that Florida fundraiser, instead breaking out the heavy rhetoric to loosen some wallets. We wonder about the political wisdom of slapping at that 47 percent, given that CNN surveys showed a not-so-insignificant four of 10 people who made $30,000 or less voted Republican in 2010. The remarks also won’t play well with moderates who pay federal income taxes and believe we should care about, not dismiss, the struggles of those who don’t.

Those moderates, unfortunately, are a dwindling group. Studies show Americans following the lead of elected officials and becoming more hostile not only toward opposing political parties, but groups such as immigrants and minorities. In other words, each other. That hostility is fueled by both sides – by demonizing people who might legitimately need government benefits, but also by scorning the affluent who don’t want to contribute their “fair share” of taxes.

Now Mitt Romney waves a dismissive hand at half of America, then defends the remarks as merely “not elegantly stated.” They were more than that. They were untrue. And sadly, they fed our growing appetite to believe the worst in each other.