Senate Republicans set on reworking the Affordable Care Act are considering taxing employer-sponsored health insurance plans, a move that would meet stiff resistance from companies and potentially raise taxes on millions of people who get coverage on the job.

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The move could raise billions in revenue that could be used to help stabilize the fragile individual insurance market. But it could be politically risky, since it could expand the impact of GOP health proposals from Medicaid recipients and those who buy insurance on their own to the roughly 177 million people who get coverage through their employers.

A number of lawmakers are open to the idea, including Sen. Mike Lee (R., Utah), GOP aides said, but there is no consensus yet on whether it should be included in the draft bill being written during this week's congressional recess.

Under longstanding tax law, compensation in the form of health insurance isn't treated as income for workers. That means employers can deduct the cost and the value isn't subject to payroll taxes or individual income taxes. It is a system that economists say distorts the market in favor of generous insurance packages, but like other tax breaks, it has proven popular and difficult to dislodge.

Previous efforts to end the tax break have faltered. House Republicans, in crafting their version of the health bill earlier this year, considered limiting the amount companies could exclude from employees' income for health coverage, but dropped the idea when it faced an immediate pushback.

Business groups opposed the House proposal vigorously, and many House Republicans expressed alarm over the practical and political impact.

"Most of America gets their insurance through the workplace," said Rep. Warren Davidson (R., Ohio) in an interview Thursday. The House proposal "was an overhaul of the only part [of the health system] that isn't broken inherently," he said.

House Speaker Paul Ryan (R., Wis.), who floated the idea in his own health proposal, has said the tax code unfairly favors people who get their health insurance through work over those who buy it on their own. Republicans, Mr. Ryan said in March, want to "stop the discrimination in the tax code against people who want to go out in a free marketplace and buy the health care of their choosing."

A spokesman for Sen. Lee said he was open to a tax on employer plans but wasn't ready to commit to supporting anything until he saw the details, particularly how the revenue would be used.

Republicans are hoping to get the health-care law passed in the Senate by the end of June, an ambitious goal given that they have yet to reach consensus on key policy issues.

Nearly all premiums for employer-provided insurance are excluded from federal income and payroll taxes, an arrangement that cost the federal government more than $250 billion in fiscal 2016, according to the nonpartisan Congressional Budget Office. The portion of premiums paid by employees is often also excluded from taxable income.

The exclusion gives employers an incentive to offer more generous coverage, and economists say that raises total premiums and encourages unnecessary spending. Companies and unions who have fought to retain the exclusion say taxing the plans would prompt employers to scale back benefits, pass the cost of the tax to workers, or stop offering coverage altogether.

Despite the political risk, the idea appeals to some senators because it could bring in a lot of money. That is critical because the health bill must achieve at least $119 billion in budgetary savings over the next decade, under Senate procedures allowing the legislation to pass with a simple majority.

Republicans in both chambers have long favored limiting the exclusion but recognized the political risk. "If you start taxing workers for health benefits, you're really expanding the number of people affected by these proposals," said Larry Levitt, a senior vice president at the Kaiser Family Foundation.

Discomfort with the tax-free status of employer-sponsored health coverage isn't limited to Republicans. Former President Barack Obama supported a 40% levy on generous employer plans, though that move, known as the Cadillac tax, has been delayed by Congress until 2020.

--Richard Rubin contributed to this article.

Write to Stephanie Armour at stephanie.armour@wsj.com and Kristina Peterson at kristina.peterson@wsj.com