The Obama administration has found a way to give unions relief from an Obamacare tax nearly three weeks after Republicans rejected a Democratic push to include the labor carve-out in the latest budget deal.

The Department of Health and Human Services quietly released a final rule last week that includes an intention to exempt some union insurance plans from a substantial new tax known as the reinsurance fee.

As part of Obamacare, the tax was supposed to be levied against all insurance plans to share the risk for insurers taking on the sickest patients next year.

But unions, which were among the strongest supporters of the Affordable Care Act when it passed in 2010, had pressed the administration for changes to the law, arguing that the measure is harmful to insurance plans accessed by more than 15 million union members and would raise costs.

Before last week, unions were upset that the Obama administration had failed to grant them a carve-out even after delaying a requirement that all businesses with 50 employees or more offer health insurance or pay steep fines to 2015.

In July, union leaders -- including Teamsters President James Hoffa -- wrote a letter to Senate Majority Leader Harry Reid, D-Nev., and House Minority Leader Nancy Pelosi, D-Calif., warning of “nightmare scenarios” for millions of workers if the law is not changed to accommodate labor health plans.

“Congress wrote this law; we voted for you,” they wrote. “We have a problem; you need to fix it.”

The AFL-CIO adopted a resolution at its September convention that it would seek a union exemption from the reinsurance fee, along with ACA tax credits for low-income members.

Deep into a rule governing Obamacare issued last week, HHS included language that the administration will propose exempting “certain self-insured, self-administered plans” from the law's reinsurance fee in 2015 and 2016, Kaiser Health News first reported Wednesday.

The oblique reference applies to some union plans that act as their own insurance company and claims processor.

An HHS official said the exemption is only in the proposal stage.

“We intend to solicit comments from interested parties and the general public about whether to permit such a limited exemption when we issue the proposed rule,” the official said.

During last month's budget negotiations aimed at re-opening the government and avoiding a default on the nation's debt, Reid pushed a similar union fix in exchange for Republicans winning a provision that would require a minimum income level for receiving some Obamacare subsidies.

But many conservative Republicans considered the union fix an overreach on the part of Democrats and rejected it during final negotiations on the budget deal.

In mid-September, a group of 21 Republican senators led by Sens. Lamar Alexander, Tenn., and Orrin Hatch, Utah, urged the administration not to give unions an unfair Obamacare fix.

The senators sent a letter to Office of Management and Budget Director Sylvia Burwell urging her “not to authorize the release of any regulations that will create a special carve-out that benefits union workers at taxpayers' expense.”

Conservative groups opposed to any Obamacare carveout for unions called the latest effort by the administration unfair because it sets up different rules for different groups of insurance plans and offers no relief for individuals subject to fines for not having insurance.

“It's outrageous that the Obama administration is ignoring the plain language of the law he insisted on to deliver another bailout to the union bosses,” said Fred Wszolek, spokesman of the Workforce Fairness Institute. “Either follow the law and tax every insurance plan, or repeal the whole thing, but there's no legal basis for another expensive favor for big labor.”

The reinsurance fee is $63 per person covered by an insurance plan per year, and is expected to raise $25 billion over three years. Exempting unions in 2015 and 2016 from the tax would protect their plans from taking a major hit, although they would have to pay it in 2014, when the tax will be the greatest during the first year Obamacare is in effect.

This story was published at 2:40 p.m. and has been updated.