The disastrous debut of Obamacare and the ever-tighter alliances between public unions and the Democratic Party’s antigrowth factions—especially environmentalists—have further alienated private-sector labor leaders.

The head of the American Federation of Teachers, Randi Weingarten, went so far as to offer a local labor official $1 million in union campaign support to take on Emanuel, up for reelection in February. But private unions have a different view of the mayor.