There's more than a touch of absurdity in the way an industry fee in President Barack Obama's health care law is being passed along to state taxpayers.

As Alice in Wonderland might say, a curious tax just got curiouser. The burden to states could mount to $13 billion in less than a decade.

The Health Insurance Providers Fee was aimed at insurance companies. The thinking went: Because insurers would gain a windfall of customers, they ought to help pay for the expansion of coverage. Insurers say they have raised prices for individuals and small businesses to cover the new tax.

As it turns out, they are raising their prices to state Medicaid programs, too.

The federal government issued guidance in October requiring states to build the tax into what they pay for-profit Medicaid health plans that serve low-income people. The first year's tax was due to the IRS in September, and state governments are now settling up with insurance companies.

It works like this: State governments pay insurers for the tax. The insurers then pay the tax to the federal government. The federal government then reimburses part of the cost to the states.

It may sound absurd, but it's not amusing to state governments, which wind up losing 54 cents for every dollar of the insurance tax. State taxpayers end up the biggest losers, without any added benefit to their state's low-income Medicaid patients.

"It's like a merry-go-round with an extra loop in the middle," said Rebecca Owen of the Society of Actuaries.

The extra loop? The health law tax is not deductible for the insurance companies when they file their corporate income taxes, and state governments must kick in extra to cover that cost, too.

"If they're following the standard of practice, there's no wiggle room" for states to shift the burden back onto the companies, Owen said.

It's particularly troubling because more states are turning to private sector Medicaid managed care to keep health care costs down. An estimated 70 percent of Medicaid patients are covered by these types of plans.

Insurers such as Anthem, UnitedHealth and Centene manage the care of millions of low-income people in taxpayer-funded programs.

The fee on health insurance companies was one of several new taxes Congress used to pay for the health care law.

"They had a naive notion we were going to get something from insurers" who were gaining many new customers from the health law, said economist Douglas Holtz-Eakin, president of the American Action Forum, a center-right public policy institute. "It defied any notion of good tax policy."

Most nonprofit insurers are exempt, but there's no exemption for profit-making Medicaid managed care companies that collect payments from state governments with the promise of providing better care at lower costs.

The states with the most managed care will be hurt the most. Florida will pay up to $1.2 billion over 10 years, according to a 2014 report by the actuarial firm Milliman. The same for Pennsylvania. Texas will pay up to $1 billion and Tennessee as much as $884 million. For California, the decade's total will be up to $798 million and for Georgia, $647 million.

The Milliman report estimates Illinois will pay $394 million to cover the tax through 2023. Illinois is starting to make higher payments to cover the tax, even as Gov. Bruce Rauner has proposed making $1.5 billion in cuts to Medicaid providers such as hospitals for the upcoming budget year.