Senate Majority Leader Mitch McConnell (R-Ky.) alongside other GOP leaders at the Capitol last month. (J. Scott Applewhite/AP)

A new tax break for the upper middle class was offered up Thursday in Senate Republicans' revised version of their bill to dismantle the Affordable Care Act, also known as Obamacare.

The legislation would make health insurance premiums more affordable for consumers who buy the kinds of inexpensive policies that are crucial to the GOP health-care agenda. Yet independent analysts caution that the benefits would mainly accrue to affluent households, and the provision might not substantially expand coverage among the uninsured.

The language relates to health savings accounts (HSAs), vehicles that allow consumers to set aside a portion of their income without it being taxed and then use that money to pay for medical expenses.

Currently, the accounts can be used only for out-of-pocket costs, such as insurance deductibles and co-payments. The GOP bill would allow owners of these accounts to use the money to pay for premiums as well. Doing so would make the accounts much more attractive, allowing taxpayers to claim a break on a major monthly expense rather than only on their out-of-pocket costs for doctor visits and other health-care items.

The provision would primarily benefit more-affluent households, in part because they are the ones that can afford to divert money into the accounts. And because marginal rates on income are steeper for wealthier taxpayers, they save more when they are able to write off an expense and reduce the income on which they have to pay taxes.

About 44 percent of households — mostly those that are less well off — do not pay any federal income tax, according to the nonpartisan Tax Policy Center. Very few households in that group would benefit from being able to pay premiums out of health savings accounts.

Additionally, the most important benefits would go to people who are too affluent to qualify for the federal subsidies that would be available to help modest-income households buy private coverage on the individual market. Since the subsidies cover part of the cost of premiums, those who receive them would be able to deduct less from their incomes.

Under the GOP bill, the subsidies would be available to households at up to 350 percent of the federal poverty level, or about $71,000 for a family of three.

For that reason, critics of the GOP bill were skeptical that the change with HSAs would help uninsured Americans obtain coverage, noting that many who would be wealthy enough to benefit meaningfully already have insurance — coverage typically through an employer.

“It’s going to provide the greatest benefits to higher-income people who already can afford health insurance, so it’s not going to do much in the way of helping people afford coverage who are going to lose it,” said Edwin Park, a vice president for health policy at the liberal Center on Budget and Policy Priorities.

The Joint Committee on Taxation (JCT) and the Congressional Budget Office (CBO) — the two nonpartisan agencies responsible for supplying lawmakers with information about federal taxes and spending — have forecast in a preliminary analysis that the latest change to the rules around health savings accounts would increase coverage, according to a Senate aide. A precise estimate was not yet available on Thursday, however.

Predicting exactly how the provision would affect the number of uninsured Americans would be extremely difficult, outside experts said, and the result would depend on how the change would interact with other revisions. For instance, another element of the bill — put forward by Sen. Ted Cruz (R-Tex.) — could also make health savings accounts more common.

Under current federal law, the accounts are available only for people who purchase plans with higher deductibles. Cruz's proposal would make it easier for insurance companies to offer such policies, and if health savings accounts were more widely available because of the GOP legislation, more people might take advantage of the opportunity to write off their premiums.

As a result, the number of people who would benefit depends on how attractive the cheaper offerings would be under the Cruz proposal relative to the individual plans that would comply with the ACA's essential health benefits.

Since policymakers have to date not allowed taxpayers to pay for insurance out of their health savings accounts, any forecasts are part guesswork. That is true not only for the number of people who might take advantage of the new system but also for how much revenue the federal government would lose.

“I’m really reluctant to guess how much it’s going to cost,” said Linda Blumberg, an economist at the nonpartisan Urban Institute. “I don’t think it’s going to be huge money necessarily, but I think it’s going to have an impact.”

Tom Miller, an economist at the right-leaning American Enterprise Institute, said, “It will be a pretty imprecise guess.”

“The only number that will matter will be supplied” by the CBO and JCT next week, he noted. The two agencies will release a comprehensive analysis of the revised bill.

That new version would keep several of the ACA taxes paid mainly by the very rich. Initially, GOP lawmakers had proposed repealing those.

One is a levy on the salaries of people earning more than $200,000 a year as individuals, or $250,000 for married couples. The other taxes are a surcharge on certain investments for households in that income category and what is effectively a special tax on the compensation executives receive from their firms in the insurance industry.

Correction: An earlier version of this story incorrectly stated that households that do not pay federal income tax would not benefit from being able to pay premiums out of health savings accounts. While very few households in this group would likely benefit, it is possible that some could receive a larger Earned Income Tax Credit, for example. This version has been corrected.