The only thing standing between minimum wage employees and a generous salary with paid time off is the greed of the large corporations they work for. That's the argument voters in SeaTac, Wash., will consider Nov. 5 when they vote on a referendum to create a $15 minimum wage—more than twice the federal minimum of $7.25.

This corporations-can-afford-it narrative isn't confined to the Pacific Northwest. Earlier this year, groups like Fast Food Forward, backed by the Service Employees International Union, organized walk outs at large restaurants in major cities and presented the same $15 demand, arguing that "it's time for these big fast-food and retail companies to pay up."

It's a clever talking point designed to shift the focus from the size of the wage mandate to the size of the employer. But it doesn't square with the facts.

In March each year, the Census Bureau conducts a special survey of many of the same U.S. households that make up the monthly jobs report. Respondents are asked about the size of the company they work for, and the responses are then sorted into six categories ranging from fewer than 10 employees to 1,000 or more.

In a recent analysis, the Employment Policies Institute used this data to determine the size of a typical minimum-wage employer. Contrary to the rhetoric of organized labor and its allies, the vast majority of people earning the minimum wage aren't working at large corporations with 1,000 or more employees. Roughly half the minimum-wage workforce is employed at businesses with fewer than 100 employees, and 40% are at very small businesses with fewer than 50 employees.

The results are similar even if you follow the left's cue and broaden the analysis from minimum wage employees earning $7.25 an hour to "low-wage" employees earning $10 an hour or less: 46% still work for businesses with 100 or fewer employees.

Some of these businesses are small diners or independent grocery stores; others are franchisees that own a handful of stores affiliated with a recognizable brand. (For instance, over 80% of McDonald's locations are owned by franchisees.) In either case, the profits and executive pay at the country's largest businesses have nothing to do with the stark economics these small-business owners face: single-digit profit margins, extremely price-sensitive customers, and no room to absorb a substantial increase in the minimum wage without dramatically reducing the cost of service.

These facts are important because the contrast between corporate pay and entry-level wages is a linchpin in the liberal argument for a higher minimum wage. "Many corporations are posting record-breaking profits," complains the SEIU-backed National Employment Law Project. "They can afford to pay better."

Even President Obama has gotten in the act, arguing that "CEO pay has never been higher" to support his call for a higher minimum wage. The small-business owners that would actually bear the brunt of the president's good intentions are surely scratching their heads at this case of mistaken identity.

Even if the talking point was true, and large corporations were mostly responsible for the country's minimum wage workforce, organized labor's math still wouldn't make sense. Profit margins are determined more by the business model than the size. According to Deloitte's Restaurant Industry Operations Report, the median profit margin at an independently owned fast-food restaurant is 2.6%—and only about a percentage point more at a corporately-owned location. The corporate locations might have more of a cash reserve than their independent counterparts, but any labor cost increase is also magnified across a larger workforce.

The large corporate villain is unlikely to disappear off the public stage anytime soon. It's proved an effective boogeyman in campaigns on health care, paid time off, and a host of other union priorities. It's disappointing, but not surprising: In labor's political campaigns, truth is always the first casualty.

Mr. Saltsman is research director at the Employment Policies Institute.