The Supreme Court might be about to blow a hole in Obamacare large enough to fit nearly 10 million people, a new analysis shows.

The high court is scheduled to hear arguments this March in a lawsuit claiming President Barack Obama’s administration does not have the legal authority to give tax credit subsidies to millions of people who have insurance under the Affordable Care Act. The argument is over a small bit of wording in the law, which says subsidies can go to people buying insurance on state-run marketplaces, but not to people buying on federally run ones.

Since the federal government operates the exchanges in two-thirds of the states, a ruling for the plaintiffs would gut the Affordable Care Act.

The result: 9.6 million people living in 34 states would be forced to give up their health insurance policies, according to a report issued Thursday by the Rand Corp., a nonprofit consulting firm and think tank. That’s 70 percent of the 13.7 million people Rand projects will have health insurance through the exchanges this year. The administration projects 9.1 million enrollees this year; 70 percent of that total would be 6.4 million people.

This latest legal challenge to the Affordable Care Act, called King v. Burwell, alleges that seven words in the statute — “through an exchange established by the state” — signify that only state-run health insurance marketplaces are permitted to dole out federal subsidies. The Obama administration, along with the congressional Democrats who wrote the law, reject this argument, and contend a full reading of the statutory language makes plain the ACA’s intent is to provide subsidized health coverage to low- and middle-income households in every state.

The Supreme Court agreed to hear this case, one of several similar ones, in November, even though no federal appeals court had ruled in the plaintiffs’ favor. Previously, the administration asked the justices to postpone any consideration of the suits until appeals courts issued different decisions. The Supreme Court upheld the Affordable Care Act in another major case against it in 2012, when conservative Chief Justice John Roberts joined four liberal justices in a 5-4 ruling.

The dire effects of a ruling against Obamacare subsidies in states with federal exchanges wouldn’t be limited to the people who get tax credits, Rand economists Evan Saltzman and Christine Eibner conclude. At least 85 percent of enrollees get financial assistance via the federal health insurance marketplaces.

In addition to low- and middle-income subsidy recipients finding their health insurance policies unaffordable, unsubsidized customers also would be affected. The sudden withdrawal of 70 percent of enrollees, including large numbers of young and healthy policyholders, would trigger a chain reaction known in industry jargon as a “death spiral.”

Health insurance companies would respond to the exit of so many customers, especially the more price-sensitive healthy ones vital to keeping overall costs down, by raising prices. Those high prices would then drive out more consumers, and those who are most expensive to insure because of poor health would be likeliest to remain. That, in turn, would lead to higher costs for insurers, causing them to further increase prices, or to leave exchanges entirely. For a 40-year-old nonsmoker, the premium for a mid-level “Silver” insurance plan initially would jump from $3,450 to $5,060 a year, the study says.