Walmart unionization is the Holy Grail of organized labor; Walmart is the largest private employer in the U.S. and, indeed, the world (it has a reported 2.1 million workers total, about two-thirds of them in America) and has a notoriously bad reputation for low wages, poor benefits and workplace discrimination.

Walmart has managed to keep its stores union-free, perhaps aided by a bad economy in which many consider a crummy job better than no job at all. But in recent weeks, the company has been grappling with a worker uprising, as a small but growing number of employees have gone on strike at stores in California, Dallas, Seattle, Miami and Washington, D.C.

The walkouts, which began in Los Angeles, are organized by OUR Walmart (that stands for Organization United for Respect at Walmart), a union-backed group that’s calling for better treatment of employees.

“We envision a future in which our company treats us, the Associates of Walmart, with respect and dignity,” the group says. “We envision a world where we succeed in our careers, our company succeeds in business, our customers receive great service and value, and Walmart and Associates share all of these goals.”

At deadline, the strikes hadn’t spread to New England. But local activists have been showing their support, last week leafleting at Valley Walmarts. At the Hadley store, for instance, the Raging Grannies sang by the entrance while fellow activists handed out flyers charging that the company has retaliated against workers who’ve spoken out about problems at the stores. The group also urged shoppers to sign a petition, at www.ForRespect.org, calling on Walmart to “respect [employees’] freedom of speech.”

Walmart officials are downplaying the actions; a spokesman for the company told ABC News that most workers there don’t want to join unions, saying, “They seem to recognize that Walmart has some of the best jobs in the retail industry—good pay, affordable benefits and the chance for advancement.”

It remains to be seen how sanguine the company will be if workers follow through on the threat, issued last week, to walk out on the day after Thanksgiving, the crazy shopping day known as Black Friday.