The governors of New York and New Jersey planned a cover story to contain political fallout from the massive traffic jams caused by lane closures on the George Washington Bridge, the government’s star witness testified Tuesday.

David Wildstein, a former Port Authority official, told jurors that New York Gov. Andrew Cuomo and New Jersey Gov. Chris Christie spoke in October 2013, a month after the lane closures. They agreed that a report would be issued stating the lane closures were a traffic study, and that the New Jersey...