Gallup also found slightly more than half those surveyed predict unions will become weaker, with only about one in five thinking they'll be stronger in the future.
Nowadays, fewer people have family roots in organized labor, and that colors the perception of unions. "The image goes back and forth between non-existent and the boogeyman," says Cowie, the Cornell historian.
The image in recent years has been shaped by skirmishes in the public arena, where union membership is nearly 36 percent. Massive protests in two industrial Midwest states in 2011 ended with opposite results.
In Ohio, voters overwhelmingly rejected a sweeping law that placed restrictions on public employee unions â¿¿ a huge victory for labor. But in Wisconsin, the GOP-controlled Legislature approved Gov. Scott Walker's proposal that effectively ended collective bargaining for most public workers â¿¿ a move that sparked an unsuccessful gubernatorial recall.
The Wisconsin law may have long-term ramifications. The number of unionized public workers there fell by about 48,000 in 2012 â¿¿ about a quarter of the total, according to an analysis by Barry Hirsch, a labor economist at Georgia State University.
That suggests the incentive for being in one of those unions is now much weaker, Hirsch says, but it's too early to tell if that will be a trend.
Meanwhile, organized labor is fighting to extend its reach in the private sector, including in the South, generally hostile turf for unions.
The UAW has lost two bids to organize workers at the Nissan Motor Co. auto plant in Smyrna, Tenn. The union is now trying to get the Japanese automaker to allow it in the plant to make its case to workers in Canton, Miss.
Black ministers, college students, the NAACP and political leaders, with an assist from actor Danny Glover, have formed an alliance, staging press conferences, holding rallies and making TV appearances, casting the campaign as a civil rights battle.