Sens. John Thune, R-S.D., Orrin Hatch, R-Utah, and Lamar Alexander, R-Tenn., introduced a bill Tuesday that would prohibit the administration from granting tax exceptions from Obamacare to multi-employer health insurance plans. The bill is called the Union Tax Fairness act in recognition of the fact that most such plans are managed by organized labor.

Citing media reports that the administration was considering an exception for the Affordable Care Act's so-called "reinsurance fee," the senators said such a deal would be unfair favoritism to Big Labor. Nine other Republicans are co-sponsoring the bill.

"Unions should not be granted a special exemption from Obamacare's reinsurance tax just because the president fears further union backlash on his signature law. These unions agreed to pay this tax when they endorsed Obamacare, but now that they are finding out what the law means for them and their plans, they want out. Rather than granting special backroom deals to political allies, the administration should support fairness for all by permanently delaying the law for every American," Thune said.

Unions have pushed hard to waive the tax for multi-employer plans. Reports of a deal have swirled since midsummer and intensified last month.

The Washington Examiner's Phil Klein explained the problem for unions last month:

The proposed deal would include a one-year delay in a fee strongly opposed by unions that was to be assessed against health insurance plans starting in 2014, according to Politico.

The relevant provision of President Obama's health care law, the Transitional Reinsurance Program, was set up as a way of preventing any given insurer from getting stuck with a disproportionate number of very sick individuals with high medical expenses now that they're forced to offer insurance to all comers.

The intention was for the federal government to collect $25 billion in fees between 2014 through 2017 to fund partial reimbursement of insurers for taking on added risk. The fee was supposed to be $63 per plan participant in 2014.

But unions strongly opposed the fee as a tax on the generous health care benefits they won through negotiation with private sector employers.