WASHINGTON — The Obama administration sneaked in a rule that would let some labor unions off the hook for an ObamaCare tax.

After publicly rejecting the unions’ request for an exemption, the Department of Health and Human Services last week quietly gave the unions a pass on what would have been a massive tax hit.

The tax, known as the reinsurance fee, requires self-insured organizations, such as unions and some large companies, to pay $63 for each covered member and an additional $63 for each additional family member on a health plan.

The fee was expected to raise $25 billion over three years, with the funds going to insurance companies to offset the cost of covering pre-existing conditions and other mandatory benefits.

Sparing unions that expense will go a long way toward repairing President Obama’s strained relationship with labor.

The unions, originally key supporters of the president’s health-insurance law, have increasingly bucked ObamaCare as it threatens their finances and the generous policies enjoyed by some of their members.

Buried in the new rules is a proposal to exempt “certain self-insured, self-administered plans” from the fee in 2015 and 2016.

That description applies to many union plans, according to experts.