ON Labor Day in 1960, John F. Kennedy kicked off the final push of his presidential campaign in Cadillac Square in Detroit with a rousing speech to thousands of United Auto Workers members. It was a nod to the immense clout of organized labor.

Those days are long gone. Today about 11 percent of American workers belong to unions, down from 31 percent in Kennedy’s day. And that powerful autoworkers union? Its membership has plummeted to 400,000 from a peak of 1.5 million in 1979. The declines have been particularly steep in former strongholds like Michigan, which holds its primary on Tuesday, as well as Ohio, Illinois, Wisconsin and other Rust Belt states that will hold primaries in the coming month.

With its shrinking ranks, organized labor, which tilts strongly Democratic, was already struggling to compete with Republican-leaning “super PACs” financed by wealthy conservatives like the Koch brothers, who have vowed with their allies to spend $889 million on this election. Now the labor movement is being buffeted by another force: Donald J. Trump, whose attacks on trade deals, illegal immigrants, Chinese imports and the shifting of jobs overseas are winning over white, blue-collar workers.

Can a weakened labor movement still provide the money, voters and get-out-the-vote muscle to elect the Democratic nominee in crucial swing states, as it has in the past?