Capitol Hill Republicans are trying to stop the Obama administration from offering labor unions a sweetheart deal on ObamaCare, as the White House tries to quell a simmering rebellion from Big Labor over the health care law.

President Obama and White House officials reportedly have called union leaders to try and persuade them to tone down their complaints, pledging an accommodation. The AFL-CIO, though, on Wednesday approved a resolution anyway calling the law "highly disruptive" to union plans.

But reports have surfaced on a plan that would give union workers -- and only union workers -- subsidies to help pay for health insurance even if they're covered through their job. The purported "carve-out" could soothe the simmering discontent within Big Labor. The loyal Democratic supporters and early champions of ObamaCare say they have been slighted by the act’s final regulations, which they say is pushing some employees into part-time work and threatens their health insurance plans.

At least three congressional Republicans are trying to stop any effort to give the unions special treatment, which could cost $200 billion over 10 years.

Sen. John Thune, R-S.D., on Monday introduced the "Union Bailout Prevention Act," which would stop the granting of subsidies to offset premium costs for the multi-employer plans held by many union members. Separately, the House voted on Thursday to stop all subsidies until the administration launches a system to verify recipients are eligible.

Big Labor argues that workers without additional subsidies will switch to less-expensive, major-insurer plans, creating a withering effect on the so-called Taft-Hartley plans.

Thune and others argue the plans are already government-subsidized and the workers’ contributions are already tax-exempt.

“A deal such as this by the administration for the union would be illegal,” Utah Sen. Orrin Hatch and Michigan Rep. Dave Camp said in a letter Tuesday to the Treasury Department. “Giving union workers exchange subsidies in addition to the income-tax exclusion would be double dipping.”

News reports about the plan have been circulating for days, including an early one by the Inside Washington news service. The Health and Human Services Department did not return calls or emails from FoxNews.com asking about the veracity of those reports.

Labor unions launched a multi-targeted attack this summer to force changes to ObamaCare, including one on the mandate for employers to offer insurance to full-time employees, which they say has resulted in more part-time jobs. Though that provision has been delayed, the concern is that employers are shaving the number of full-time employees in order to stay under the law's threshold for when they have to start offering coverage.

“Unless you and the Obama administration enact an equitable fix, the (Affordable Care Act) will shatter not only our hard-earned health benefits, but destroy the foundation of the 40-hour work week,” union leaders wrote in a letter this summer to congressional Democratic leaders.

The letter, co-signed by the Teamsters union, was sent to House Minority Leader Nancy Pelosi, Calif., and Senate Majority Leader Harry Reid, Nevada, and followed a resolution by a Nevada chapter of the AFL-CIO hammering on the same issues.

“The unintended consequences of the ACA will lead to the destruction of the 40-hour work week … and force union members onto more costly plans,” the resolution stated.

Labor unions also feel slighted because low-income Americans are eligible for subsidies to help them purchase insurance through exchanges or marketplaces created by ObamaCare, when enrollment begins Oct. 1.

“Other stakeholders have repeatedly received successful interpretations for their respective grievances,” the unions told Pelosi and Reid in the July letter.