The poll found that an overwhelming 71 percent of Democrats opposed weakening collective bargaining rights. But there was also strong opposition from independents: 62 percent of them said they opposed taking bargaining rights away from public employee unions.

Phil Merritt, 67, a retired property manager from Crossville, Tenn., who identifies himself as an independent, explained in a follow-up interview why he opposed weakening bargaining rights for public workers. “I just feel they do a job that needs to be done, and in our country today if you work hard, then you should be able to have a home, be able to save for retirement and you should be able to send your kids to college,” he said. “Most public employees have to struggle to do those things, and generally both spouses must work.”

The one group that favors weakening those rights, by a slim majority, was Republicans. Warren Lemma, 56, an electrical contractor from Longview, Tex., said states did not have the money to pay for many benefits that state workers enjoy.

“Retirement benefits should not be taken away from those about to retire, but the system should be changed for the people starting to teach just now,” said Mr. Lemma, a Republican. “And the only way the system will change is to do something about unions and their control, and the only way to do that is to take away collective bargaining.”

The poll found that 45 percent of those surveyed said they believed that governors and state lawmakers who are trying to reduce the pay or benefits of public workers were doing so to reduce budget deficits, while 41 percent said they thought they were doing so to weaken unions’ power.

Although cutting the pay or benefits of public workers was opposed by people in all income groups, it had the most support from people earning over $100,000 a year. In that income group, 45 percent said they favored cutting pay or benefits, while 49 percent opposed it. In every other income group, a majority opposed cutting pay or benefits: Among those making between $15,000 and $30,000, for instance, 35 percent said they favored cutting pay or benefits, while 60 percent opposed it.

Labor unions, including private sector labor unions, are seen as less influential now than they were three decades ago. The poll found that 37 percent of those surveyed believe that labor unions have “too much influence” on American life and politics, while 48 percent said they had the “right amount” or “too little” influence. In a 1981 poll, by contrast  soon after President Ronald Reagan fired striking air traffic controllers  60 percent of those surveyed said unions had “too much influence.” Of course, union membership has declined since then.