For most of the year, when attacking President Obama on the economy, the Romney campaign has relied on a distorted approach to counting jobs: Rather than start the count from when Obama’s policies took effect — which gives you a decent sense of how many jobs the administration has “created” — Team Romney blames Obama for the first six months of 2009, when the economy was still plummeting. This allows them to say that Obama has “presided” over net job losses, ignoring the fact that he entered office during an economic free fall.

Sometime during the summer, the Romney campaign backed away from this approach, opting instead for attacks on Medicare and welfare reform — where Mitt Romney has falsely accused Obama of “gutting” the program. But now that the conventions are over and Obama has established a solid lead in the election, Romney has decided to go back to his original approach, in hopes that he can make this election about the economy again.

As such, the campaign has released a new ad — “Failing American Workers” — that blames the president for the growth in Chinese manufacturing capacity. The key claim is straightforward, “Under Obama, we’ve lost over half a million manufacturing jobs.”

Like Obama’s attacks on Bain outsourcing, there’s no way that this is sincere. I highly doubt that Mitt Romney — a former private equity manager — has any qualms about outsourcing. But he is concerned about losing, and in particular, he’s concerned about losing Ohio, where Obama leads by an average of nearly 3 points. Without Ohio, Romney’s path to victory becomes much more narrow — he’d have to win Florida, Virginia, Colorado and several other swing states to reach 270 electoral votes.

This ad, like Jennifer Granholm’s speech last week at the Democratic National Convention, is an obvious appeal to the working-class whites who predominate in Ohio and who are critical to Romney’s chances nationwide.

Of course, there’s an obvious problem with this line of attack; it’s completely false. Yes, if you begin in January 2009 — when 1,255,200 people worked in manufacturing — and subtract from August 2012 — when that number stood at 1,197,000 — you’ll see a net loss of manufacturing jobs. But if you measure from when the stimulus began to take effect — second quarter 2009 — then you’ll see a manufacturing sector that’s grown by more than 100,000 jobs. If you compare to January 2010, when Obama’s policies were fully in effect, then there are 512,000 more manufacturing workers.

In terms of where Romney should be aiming, this is an improvement over the last week of flailing over foreign policy. But the dishonest suggests desperation — an attempt to find any advantage over Obama. Given that this is the phase when voters begin to settle on their choices, I have my doubts that it will work.

Jamelle Bouie is a staff writer at The American Prospect. You can find his blog here.