President Barack Obama’s loyal allies in the labor movement aren’t jumping to help the administration in the public battle over the problematic Obamacare website.

Put off by new reinsurance fees on group health care plans that affect union members, Big Labor is largely sitting out the effort to enroll people for health care coverage or make the White House’s public case that the mangled rollout of HealthCare.gov doesn’t mean the entire Affordable Care Act is flawed.

The AFL-CIO isn’t lifting a finger to help the White House — it remains in negotiations at the White House and on Capitol Hill to change elements of the law it finds objectionable to workers. Those talks were put on hold earlier this month during the government shutdown — a far larger concern for the federal government employee unions — and have begun to restart only in recent days, according to officials from multiple unions.

Major public-sector unions also aren’t fired up to help the White House with a law that won’t affect the vast majority of their members. Nor are they ready to register people who aren’t union workers for a benefit they won’t receive themselves....