William B. Gould IV, an N.L.R.B. chairman under President Bill Clinton and a onetime lawyer for the U.A.W., said, “There is this longstanding tension between the First Amendment and the fact that the law prohibits certain types of threats and promises.” He referred to a 2011 case in which the labor board’s general counsel enraged politicians across the South by accusing Boeing of illegally retaliating against unionized workers in Washington State by opening a production line in South Carolina. This could make the Boeing case “look like small potatoes,” he said.