The narrative that Mitt Romney, left, outsourced U.S. jobs to foreign workers hurt him in 2012. Could it do the same to Donald Trump this year? (Julie Jacobson/AP)

Donald Trump’s supporters don’t care about his potty mouth, his inconsistent conservative record or his lack of specific policy proposals. Media reports on these apparent shortcomings haven’t hurt him at all.

But we’re about to find out whether one more line of reporting can blow up the Republican presidential front-runner’s main selling point — that he will “make America great again” by returning jobs to U.S. citizens, largely through mass deportation of undocumented immigrants and construction of a “big, beautiful wall” along the southern border. (Also, in a rare wonky moment for Trump, he said he would achieve this through lower taxes that would reduce corporate inversions and discourage outsourcing.)

Why would GOP voters suddenly doubt Trump’s authenticity on this promise? Well, a front-page story in Friday’s New York Times chronicles the real estate mogul’s habit of hiring foreign workers, instead of Americans, at his Mar-a-Lago Club resort in Palm Beach, Fla.

Since 2010, nearly 300 United States residents have applied or been referred for jobs as waiters, waitresses, cooks and housekeepers there. But according to federal records, only 17 have been hired.

In all but a handful of cases, Mar-a-Lago sought to fill the jobs with hundreds of foreign guest workers from Romania and other countries.

In his quest for the Republican presidential nomination, Mr. Trump has stoked his crowds by promising to bring back jobs that have been snatched by illegal immigrants or outsourced by corporations, and voters worried about immigration have been his strongest backers.

But he has also pursued more than 500 visas for foreign workers at Mar-a-Lago since 2010, according to the United States Department of Labor, while hundreds of domestic applicants failed to get the same jobs.

That’s just one article, you say — from a newspaper that many Trump supporters no doubt consider the paragon of liberal bias, no less. It won’t take hold.

Well, then came this report from NBC later Friday: "...A look into the history of the Trump Tower, the crown jewel of the real-estate mogul's empire, reveals the beginnings of the 68-story building were, in fact, rooted in the back-breaking labor of 150-odd Polish immigrants — most working illegally, some without full pay."

Ouch.

This could be merely the first swell in an upcoming wave of similar news stories. Friday’s reports followed a debate in Houston in which Marco Rubio resurrected a decades-old lawsuit brought by a New York labor union that accused the billionaire of knowingly employing 200 undocumented workers on his Trump Tower project in 1980. Trump lost, appealed and ultimately settled.

“Go online and Google it,” Rubio said. “ ‘Donald Trump, Polish workers.’ You'll see it.”

It was one of the Florida senator’s strongest moments in a strong performance, and it’s likely to inspire a quest for similar examples from Trump’s business career.

We don’t have to look back very far to see how withering the outsourcer-in-chief media narrative can be. Four years ago, Mitt Romney got pummeled by story after story about American workers who lost jobs at companies that were owned by the former Massachusetts governor’s private equity firm, Bain Capital.

To get specific, Romney struggled with the kinds of voters who today form the base of Trump’s support — less-educated, low-income laborers. These are folks who doubted Romney’s claim to be a “job creator” but believe wholeheartedly that Trump would be a great one. The only thing that could halt Trump’s march to the GOP nomination might be an erosion of voters’ faith in his ability and commitment to improve their personal economic standing -- when the populist no longer seems like he's in the corner of average U.S. workers.

Trump will surely mount the same defense that has worked so many times before on such criticisms as his donations to Democrats and his corporate bankruptcies: He was simply working the system to his own advantage as a “world-class businessman” but would work in the best interest of others as president. He freely admits to being “a greedy person”; now, however, he wants “to be greedy for our country.”

Maybe that’s the argument Romney was missing. Maybe it will continue working for Trump.

But there’s a difference between greedy habits that manifest in exploitation of arcane bankruptcy laws -- where the victim is the U.S. government -- and greed that prefers cheap foreign labor over American workers. The latter could be harder to overlook for voters who could easily imagine themselves among the rejected domestic job-seekers at Mar-a-Lago.