Here’s an unpopular opinion: Political gaffes matter.

After President Obama’s assertion Friday that “the private sector is doing fine” — and his subsequent attempt to clean up the rhetorical mess he made for himself — many Democrats insisted that while it wasn’t his best moment, it was far from consequential in his reelection race.

After all, they argued, who watches cable television in the middle of the day on a Friday? And in an election about big things — the overall health of the economy, America’s place in the world — who would ultimately care or be swayed by a single out-of-context statement made by the president? (The point Obama was trying to make, however inartfully, was that the private sector was performing far better than the public sector.)

All true. But also all missing the point.

Let’s break down the argument piece by piece.

First, while it is true that midday cable television viewership is low, that rationale completely disregards the media world in which we live, where even the smallest comment can be amplified into a national headline in minutes. Is there anyone paying even passing attention to politics who hasn’t seen the Obama clip five times at this point — which, by the way, is less than 96 hours after he said it? Answer: no.

Then there is the reality that gaffes such as the one Obama made Friday are quickly — and, usually, effectively — used by the other side to score political points. Republican presidential candidate Mitt Romney’s campaign already is out with a Web video featuring Obama’s private-sector comments juxtaposed against a series of dire testimonials from people about their economic struggles. “No, Mr. President, we are not ‘doing fine,’ ” reads the text on screen at the close of the video.

And you can be sure that the Romney campaign isn’t finished making political hay from Obama’s gaffe. Romney himself said that the comment “is going to go down in history as an extraordinary miscalculation and misunderstanding.”

(Yes, any claims that Romney makes in ads will — and should — be fact-checked by the media. But if you think that media fact-checks sway people more than scores of TV ads, I have a bridge I’d like to sell you.)

The true fight — and the truest measure of whether this gaffe will matter — is whether Romney can sell what Obama said Friday as a window into what the president really thinks. Romney is already trying to do just that, insisting just hours after Obama made the comment that the president is “defining what it means to be detached and out of touch with the American people.”

The problem for Obama is that his remark plays directly into the story that Republicans are trying to tell about him — that he is a big-government liberal who thinks the answer to all problems is expanding the federal bureaucracy and who lacks even a basic understanding of how the private sector works.

Look back at the past two presidential elections and you get a clear sense of how dangerous a single gaffe can be if it’s effectively sold as a sign of who a politician really is.

In 2004, the Democratic nominee, Sen. John F. Kerry (D-Mass.), responded to a question about opposing funding for military operations in Afghanistan and Iraq by declaring “I actually did vote for the $87 billion before I voted against it.” Republicans pounced (and kept pouncing) on the comment, arguing that it was evidence that Kerry lacked core beliefs and would say and do anything to get elected. The strategy worked as President George W. Bush (R) won a second term despite the fact that the country had already begun to sour on his leadership.

Four years later, Sen. John McCain (R-Ariz.) declared that “the fundamentals of our economy are strong” even as the financial sector teetered on the brink of collapse. The Obama campaign seized on the remark as evidence that McCain was badly out of touch and lacked the understanding necessary to help fix what ailed the country.

“John didn’t lose in 2008 because of his comment regarding the fundamentals of the economy alone,” said John Weaver, a senior adviser to the McCain campaign. “However, it did reinforce an image being portrayed by his opposition of being out of touch on such matters. The danger for the president is similar.”

For Obama, winning in November is entirely dependent on two things: convincing average Americans that he understands their economic struggles and turning the race from a referendum on his handling of the economy into a choice between the two candidates' views on how best to manage the country’s financial situation.

Obama’s private-sector comments undermine both of those arguments. And that’s why this political gaffe can — and almost certainly will — matter.