Barra and Williams declined to comment on specific issues that are expected to be central to the labor talks, including the gap between Tier 1 and 2 workers' pay and health care costs.
Williams downplayed the threat of a strike, even while saying that he's "not afraid of confrontation."
"A strike is a failure to the bargaining teams," Williams said. "It's one of the worst things that you have to do."
The contract expires on Sept. 14.