That's what happened in the original 1930s. More to the point, that's likely to happen in the modern 1930s.
Economist John Kenneth Galbraith saw unions asa "countervailing power" to greedy and overreaching managements. At no time has such countervailing power been more needed than now, following the modern 1920s.
The nation has elected President, Barrack Obama, who is notably favorable to unions. So too was his analog, Franklin Delano Roosevelt, from the Rendezvous with destiny generation. Having witnessed the destruction of unions in their respective times, they will make them safe for their kids: "My daughters will have the same opporutnity as your sons."
Jack Welch recently observed that people no longer want to work for companies. His (former) GE is a case in point, with some of the worst practices (neglect of civil rights and environmental concerns), having started on his watch. Some of these people will start their own companies (a long needed anodyne). Others will continue to "work within the system," by forming unions.
This will be until unions become as greedy and corrupt as management has recently been, like Marlon Brando's union in On the Watefront (1954). That will happen in about 20-25 years. Then there will be a middle class backlash, followed by an era that favors neither management nor unions.