The White House obviously can't pick all its fights at once, but as of yet, it hasn't picked any fights on Labor's behalf, or even shown a bare interest in doing so in the future. Some probably take that as Obama being usefully dismissive of a special interest, but in the long-run, letting Labor continue to decline is bad politics for Democrats and bad policy for workers. (Source)
Labor leadership might stick with the Dems no matter what--what other choice do they have?-- but the rank and file won't. They have good reason to think the Dems are just not their people.