The setback is a bitter defeat because the union had the cooperation of Volkswagen management and the aid of Germany’s powerful IG Metall union, yet it failed to win a majority among the plants 1,550 hourly workers.

Volkswagen workers rejected the union by a vote of 712 to 626. The defeat raises questions about the future of a union that for years has suffered from declining membership and influence, and almost certainly leaves its president, Bob King, who had vowed to organize at least one foreign auto maker by the time he retires in June, with a tarnished legacy.

“If the union can’t win [in Chattanooga], it can’t win anywhere,” said Steve Silvia, a economics and trade professor at American University who has studied labor unions.

The UAW said that “outside interference” affected the outcome of the vote. “Unfortunately, politically motivated third parties threatened the economic future of this facility and the opportunity for workers to create a successful operating model that that would grow jobs in Tennessee,” Gary Casteel, the union official in charge of the VW campaign, said in a statement.