Union membership in the U.S. workforce has withered to its smallest share since the 1940s.

Just 11.3 percent of wage and salary workers were union members in 2012, down from 11.8 percent in 2011, the U.S. Bureau of Labor Statistics reported Wednesday.

Union membership fell by nearly 400,000 workers to about 14.4 million.

More than half the decline came in the public sector as Republican-led states such as Wisconsin, Indiana and Michigan sharply curbed bargaining rights for public employees.

Other states, including Kansas, dramatically cut government payrolls. And some, such as Missouri, are considering joining nearly half the states that have “right to work” laws or related measures restricting unions’ ability to collect or use workers’ dues.

Unions last year represented 36 percent of public employees, such as teachers, police, firefighters and government agency workers, down from 37 percent a year earlier.

Losses also grew in the private sector, as union membership slipped to 6.6 percent from 6.9 percent of employees.

Furthermore, most job growth nationally — as modest as it was — occurred in nonunion companies.

The tough year for organized labor is prompting many unions to try to rally their members. Union leaders also say they’re working harder to capture the hearts and minds of the workforce at large. And some unions are taking their message to the broader public.

In the Kansas City area, electrical and sheet metal unions are running television commercials during football playoff games to point out the professional work they do on high-profile local construction projects. The carpenters’ union has published a book and is running a billboard campaign in Missouri.

Unions around the country are joining coalitions such as Jobs for Justice to augment their advocacy for broader wage and hour issues, such as minimum wage increases.

“Most in the general public see only negative stories about unions and don’t understand that we’re the ones who have negotiated workplace standards over the last century,” said Dave Wilson, business agent for the Carpenters’ District Council in Kansas City. “We’re the ones who have negotiated for fair wages, some type of retirement, some kind of health care benefits, and a safe and secure workplace.”

Union membership peaked in the 1950s, when about one in three U.S. workers belonged to a union. By 1983, the union share was down to about one in five.

Most people appreciate what collective bargaining produced historically, but they don’t look as favorably on unions today.

A Gallup poll last year found that 52 percent of the American public approved of labor unions, up slightly from the survey’s historic low of 48 percent in 2009.

Gallup has tracked public perception of labor unions since 1936, at which time 72 percent approved of unions. Approval peaked at 75 percent in 1957, and generally declined since then.

Furthermore, only one in five persons polled by Gallup expected union influence to strengthen.

“There’s a real slowing off in organizing,” said Judy Ancel, director of the Institute for Labor Studies at the University of Missouri-Kansas City.

That doesn’t mean unions are dying, she said. Instead, they’re throwing their influence into politics and social justice issues by building coalitions with other groups.

“There’s been a ceaseless, hammering attack against unions since Ronald Reagan fired the air traffic controllers in 1981,” Ancel said. “The word ‘union’ scares people because they’ve been bludgeoned to think unions are old-fashioned, corrupt money grubbers. Yet, people want raises. They want pensions. They want the rights to a hearing if they’re fired. They want the things that unions can give them.”

But most people don’t want to be union members, countered J. Justin Wilson, managing director of the Center for Union Facts, an organization funded by corporations, foundations and individuals.

That’s partly because today’s workers “are expressing a greater interest in autonomy and ambition on the job and want the ability to negotiate for themselves,” Wilson said.

It’s also because much of what unions fought for in the past “has now been codified into federal law,” Wilson said, pointing to standards required by the Occupational Safety and Health Administration and wage and hour laws.

Furthermore, federal health legislation sets health benefits standards for employers, minimizing the need for collective bargaining in that respect, he said.

“So the bargaining power of unions comes down to wages, and companies are saying it’s just not feasible to continue to pay more,” Wilson said, citing increased “givebacks” — wage concessions — by unions.

Still, the Labor Department report dramatically showed the wage-bargaining power of unions. Full-time wage and salary workers who were union members last year had median weekly earnings of $943.

That compared with median weekly earnings of $742 for full-time employees who were not union members — a $201 difference.

The new report also noted that 1.6 million workers who aren’t union members are covered by collective bargaining agreements and thus work under union-bargained terms. Those covered workers were about equally divided between public and private payrolls.

Union leaders in the Kansas City area said they were well aware of strong anti-union sentiment.

But, comparatively, “Kansas City is a good union town,” said Dave Wilson, the Carpenters’ business agent. “We take a partnership approach with our contractors: How can we add value? That’s how unions stay relevant — by adding value when we’re out there on the job.”

Gordon Clark, a member of the transport workers’ union, said he thought unions began to turn a public relations corner about five years ago, thanks partly to the Internet and cable television stations.

“If somebody wants to know something about unions now, it’s readily available on our websites,” he said. “And unions are getting more time exposure on TV, especially on the more liberal stations like MSNBC that invite presidents of the international unions on to talk about issues. That kind of exposure helps public perception.”

So, even as the percentage of union members shrinks, Clark said, unions “still have the opportunity to educate people about what collective bargaining has done and can do.”