WASHINGTON -- Union membership plummeted last year to the lowest level since the 1930s as cash-strapped state and local governments shed workers and unions had difficulty organizing new members in the private sector despite signs of an improving economy.Government figures released Wednesday show that union membership declined from 11.8 percent to 11.3 percent of the workforce, another blow to a labor movement already stretched thin by battles in Wisconsin, Indiana, Michigan and other states to curb bargaining rights and weaken union clout.Overall membership fell by about 400,000 workers to 14.4 million, according to the Bureau of Labor Statistics. More than half the loss, about 234,000, came from government workers, including teachers, firefighters and public administrators.But unions also saw losses in the private sector even as the economy created 1.8 million new jobs in 2012. That membership rate fell from 6.9 percent to 6.6 percent, a troubling sign for the future of organized labor, as job growth has generally taken place at nonunion companies."To employers, it's going to look like the labor movement is ready for a knockout punch," said Gary Chaison, professor of industrial relations at Clark University in Worcester, Mass. "You can't be a movement and get smaller."Union membership was 13.2 percent in 1935 when President Franklin D. Roosevelt signed the National Labor Relations Act. Labor's ranks peaked in the 1950s, when about 1 in 3 workers was in a union.By 1983, roughly 20 percent of workers were in unions.Losses in the public sector are hitting unions particularly hard because that's one of the few areas where membership had grown over the past two decades.About 51 percent of union members work in government, where the rate of membership is 37 percent, more than five times as high as in the private sector.Until recently, unions organizing government workers faced little resistance.That began to change when Republican Gov. Scott Walker of Wisconsin signed a law in 2011 eliminating most union rights for government workers.The state lost about 46,000 union members last year, the vast majority in the public sector.The recession of 2008 also led to much deeper cuts in state and local government than any previous recession, according to a report this month from the Nelson Rockefeller Institute of Government at the State University of New York at Albany.Since August 2008, state government employment has declined by 135,000, while local government employment fell by 546,000.Dwindling membership means that unions carry far less influence than they used to in setting a benchmark for wages and benefits that might be followed at nonunion companies. Unions are already gearing up to defeat Republican governors in Ohio, Michigan, Florida, Pennsylvania and Wisconsin.