So how bad politically for Mitt Romney — or good, depending on your perspective — is that leaked video showing Romney disparaging the Freeloading 47 percent?

Some conservatives are claiming the controversy gives Romney an opportunity to sharpen the ideological contrast with Obama. As one put it: “it worked! the media are talking about how 47% pay no income taxes.”

The flip side of this, as Kevin Drum and Ed Kilgore point out, is that conservative repetition of Romney’s argument will force a public debate over whether America is really divided between “makers and moochers,” which can’t possibly help Romney.

So who’s right? Fortunately, we have polling that can help shed light on this.

In July, Pew asked Americans what they think about the amount lower income people pay in taxes. Only 20 percent think they pay too little, versus 34 percent who say they pay a fair amount and 37 percent who say they pay too much — a total of 71 percent.

Pew also tells me that only 23 percent of independents, and 18 percent of moderates, say low income people pay too little in taxes, while big majorities of both say they pay a fair amount or too much.

Are these numbers are skewed by the large number of respondents who pay low federal income taxes or none at all? Guess what: Only 22 percent of self-described middle class people think lower income folks pay too little, versus 69 percent who say they pay their fair share or too much.

Meanwhile, the reverse is true about rich people. A majority, 58 percent, say the wealthy pay too little in taxes, while only 26 percent say they pay their fair share. Fifty six percent of independents, and 69 percent of moderates, say the rich pay too little.

What about the broader debate over the role of government and the safety net? As Jim Tankersly points out, polling suggests that swing voters actually disagree with the fundamental ideological case underlying Romney’s videotaped remarks.

This is not a good debate for Mitt Romney to have. It isn’t just that the American people overwhelmingly disagree with Romney’s theory of tax fairness and the freeloading 47 percent; it’s also that this will attract attention to one of Romney’s main weaknesses — his own wealth and low tax rates. Democrats are painting Romney as the walking embodiment of everything about our tax system that’s rigged for the rich and against the middle and working class.

It’s hard to see how the sight of the extremely wealthy Romney dismissing nearly half of Americans as freeloaders — even as he pays lower tax rates than many middle class Americans while refusing to release his tax returns so we can learn how low those rates actually are — hurts that case. This revives the class warfare debate in the worst possible way for Romney.