Unions complain consistently that the White House has ignored their requests, but the Republican lawmakers indicated that they think the administration might be on the verge of giving unions what they want.
"It appears that the administration is again planning to ignore the plain language of the statute and provide another special exemption from the law to a powerful special interest group," Camp and Kline wrote.
They pointed to a story from Inside Health Policy in which Democratic congressional aides said the administration is "working on regulations to address the issue."
The White House did not respond to a request for comment on the GOP lawmakers' suggestion that a change is imminent.
Unions' healthcare plans are currently treated like employer-based insurance, and the healthcare law does not offer subsidies to help people buy the coverage offered by their employers.
The law provides subsidies to help people afford individual policies if they do not receive coverage through an employer. Unions are asking the White House to let people use ObamaCare's subsidies to buy a union policy.