Reuter said that twice in 2012, managers talked to employees "about what it means to be unionized."
"This was in no way intimidation," he said. "It's not a threat."
The spokesman said Nissan isn't legally required to open the plant to union organizers.
"They are allowed to engage our employees outside the plant environment," he said. "We are allowed to engage our employees inside the plant environment."
One issue in the vote is Nissan's use of contract workers to perform many tasks. Employees who work directly for Nissan say they make much more than such contractors, many of whom were fired during the recession. Reuter refused to say what share of the 5,200 workers are employed directly by Nissan and how many work for contractors.
Speakers Tuesday repeatedly appealed to the heritage of the civil rights movement, noting that historically black Tougaloo College was a bastion of the fight for black rights in Mississippi.
"Dr. King said the best anti-poverty program he knew was a union," said Glover, who has repeatedly appeared in support of pro-union workers.
Student members of the Mississippi Student Justice Alliance said they were discussing the case with students at historically black colleges outside the state. They said Nissan has targeted young auto buyers, and that a pro-union youth movement would be effective.
U.S. Rep. Bennie Thompson, D-Miss., has voiced support for the union. An outside group supporting the union, the Mississippi Alliance for Fairness at Nissan, is chaired by Rev. Isiac Jackson, head of Mississippi's largest black Baptist denomination.
Mock said he's signed a card requesting a union election, but it's unclear if the UAW is close to the 30 percent required to force a vote. Unions often wait until a majority of workers or more sign cards to file for an election.
"The number of employees who are interested in unionizing is very small, in comparison to the number who are telling us they're not interested in unionizing," Reuter said.