Mr. Haslam’s office argued this week that the U.A.W. was exaggerating the importance of the leaked documents. In a statement issued on Friday, Alexia Poe, the governor’s communications director, said: “Tennessee has a significant financial investment in the plant, and in working with the company on a possible expansion, they’ve asked us to work with them on lowering labor costs and recruiting a robust supplier network. During that process, we heard concerns from suppliers and other companies about possible unionization at VW, and the governor has talked about all of those things publicly.” Mr. King also criticized Mr. Corker for issuing a statement saying that unnamed officials had assured him that Volkswagen would add a second production line if the workers voted against the union.