But the arrows are about to come flying at Target’s famous bull’s-eye logo. The nation’s largest union for retail workers has embarked on its first broad campaign to unionize Target workers.

The union, the United Food and Commercial Workers, is trying to organize 5,000 workers at 27 Target stores in the New York City area. A majority of workers at the Target store in Valley Stream, N.Y., have already signed cards supporting unionization, and a government-supervised election there on June 17 will be the first time in more than two decades that Target workers will vote on whether to join a union.

“A lot of people are going to be shocked that Target workers would consider unionizing because of its very good image and because it’s known as such a fantastic philanthropic organization,” said Burt Flickinger, a retailing consultant who has worked on projects for both the union and Target suppliers.

The union decided to focus on Target after employees in Valley Stream, on Long Island, asked for help in unionizing. Echoing longstanding complaints by some Wal-Mart workers, the store’s employees complained that many of them earned too little to support a family or afford health insurance, forcing some to rely on food stamps and Medicaid for their children.

“What we want from Target is simply this: we need a living wage where we can get by,” said Sonia Williams, a logistics employee in Valley Stream who said she earns $11.71 an hour, plus a $1-an-hour night differential.

Target says its wages are competitive and its employees do not need a union.

Interviews with 10 of the store’s employees suggest that an important issue behind the unionization drive is frustration about being assigned too few hours of work, sometimes just one or two days a week.

Retailers are increasingly assigning such short workweeks as they seek to build an extensive roster of workers to fill their ever-changing scheduling needs. But some Target workers say that means they are offered too few hours to qualify for the company’s health plan.

Ms. Williams, who receives $200 a month in food stamps to help her and her 18-year-old son, complained that she was often assigned just three days of work each week, down from full time when she started nearly nine years ago.

So far, the union’s organizing efforts have not turned belligerent as it hopes to convince Target employees that it wants to work with the company, not hurt it. In contrast, the union has never been shy about attacking Wal-Mart — hurling invective, organizing protests and lobbying officials to block the retailer’s plans to expand in New York, Chicago and other cities unless it agrees to improve wages and benefits.

Union officials assert that Target’s wages and benefits are only slightly better than Wal-Mart’s.

Jim Rowader, Target’s vice president for employee and labor relations, said the company provided “great benefits, flexible scheduling and great career opportunities for workers in all stages of life.”

He said Target emphasized building trust between managers and employees. “When you talk about bringing a union into that mix, certainly based on the culture we have and the one we’re trying to build, we don’t think a union or any third party will improve on anything,” he said.

None of Target’s 1,755 stores in the United States are unionized, nor are any of Wal-Mart’s 4,420 American stores. The union has tried over the last decade to unionize Wal-Marts in Minnesota and Las Vegas and a Target in Minnesota, but fierce antiunion campaigns by the retailers deflated the efforts before they even came to a vote.

Mr. Flickinger said unions had been loath to undertake large-scale organizing drives against retailers, like the new one against Target in New York, because of obstacles like high employee turnover, the fear of some workers that they would be fired for supporting a union and the aggressive opposition by many companies toward unionization.

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