While there was no surprise over the Supreme Court’s decision Monday to review the 2010 health-care act’s insurance mandate, supporters of the law are reeling over the justices’ announcement that they will also consider a long-shot challenge to what many consider an even more central provision of the statute.

That provision is the extension of Medicaid to cover a greater number of the poor. Twenty-six states say the expansion amounts to an unconstitutional coercion of state governments, which provide part of Medicaid’s funding.

“The decision on this issue is probably the most important the Supreme Court will be making on the Affordable Care Act,” said Ronald Pollack, executive director of Families USA, a consumer advocacy group that backs the law, referring to the statute by a common shorthand.

“Probably the most important achievement of the law is that it is going to reduce the number of people who don’t have health insurance by tens of millions. . . . About half of these people will gain their coverage through the Medicaid expansion. So the review of this provision goes right to the heart of the major accomplishment of the Affordable Care Act,” Pollack said.

Specifically, the law vastly broadens the minimum eligibility requirements for Medicaid, which provides health insurance to the poor and disabled with a combination of federal and state dollars.

Under the old rules, in exchange for federal grants that covered 50 to 80 percent of their Medicaid costs, states had to offer coverage to all children in families with annual incomes below the federal poverty level — $22,350 for a family of four — as well as to selected children with higher incomes and some adults with lower ones.

Under the health-care law, beginning in 2014, states will be required to cover all residents with incomes up to 133 percent of the poverty level, including childless adults, adding an estimated 17 million uninsured Americans to Medicaid’s rolls.

Initially, the federal government will foot the entire bill for covering the newly eligible. Its share will gradually drop to 90 percent by 2020 and beyond.

The 26 Republican state attorneys general and governors who filed the challenge to Medicaid expansion contend that these changes unconstitutionally force them to increase their spending on the program.

Already, Medicaid accounts for about 15 percent of state general fund expenditures — and in some states, the share is higher. Many states are also chafing at another requirement in the law that they maintain their current eligibility rules until the new ones take effect in 2014 — even if, as is true in many cases, a state’s standards are more generous than the current federal minimum.

Leaders of these states note that the economic crisis hit them with a double punch, depressing their revenue even as it caused their Medicaid rolls to swell with newly poor residents. At first that pain was eased by federal stimulus funding for Medicaid. But the assistance expired in June, causing states to increase their spending on the program by 29 percent in the current fiscal year.

Barred by the law’s “maintenance of effort” requirement from dropping beneficiaries from their Medicaid programs, nearly every state has turned to other tough cost-cutting measures. They have eliminated benefits, reduced payment rates to doctors and hospitals, and increased the co-payments charged to beneficiaries.

The administration contends that it has every right to revise the eligibility rules for Medicaid because it is a voluntary program. Congress gives states Medicaid funding in exchange for meeting certain conditions, and if the states don’t like those conditions, they are free to withdraw at any time. The administration can also point to a long line of court precedents upholding this “spending power” of Congress — including past challenges to Medicaid changes.

But the states party to the lawsuit argue that this Medicaid expansion is different because the amount of federal assistance at stake is so enormous and so necessary to the welfare of their most vulnerable residents that they don’t realistically have the option of giving it up.

“The [law] essentially holds the states hostage,” Paul Clement, the lawyer representing the states, wrote in a brief to the Supreme Court.

If the justices agree, advocates for the poor worry that the resulting hardship would be severe.

The “maintenance of effort” requirement alone has proved a lifesaver for children in families buffeted by the economic downturn, said Joan Alker, co-executive director of the Center for Children and Families at Georgetown University.

“Despite poverty going up for kids, the number of uninsured kids has actually gone down during these tough economic times. . . . Medicaid coverage for families who depend on it only becomes more important at a time when people are losing their jobs and having trouble finding new ones,” she said.

As for the millions of uninsured Americans who would no longer stand to gain Medicaid coverage in 2014, “these are people who under any standard are extremely needy,” Pollack said. “Right now, in 42 states adults can literally be penniless and not qualify for Medicaid.”