If congressional Republicans go through with some of the deep Medicaid cuts they are considering, three states would be left in an especially tight bind.

South Dakota, Missouri and Oklahoma have state constitutions requiring that they participate in Medicaid expansion, the part of Obamacare that expanded the health program for the poor to millions of adults.

If Republicans choose to make the projected budget reductions by cutting into Medicaid expansion, the other 37 states (and D.C.) that participate in the expansion could stop covering working-class adults. Nine states have laws explicitly requiring them to stop Medicaid expansion or make significant changes if the federal share of spending drops.

But South Dakota, Missouri and Oklahoma can’t do that. They either need to amend their constitutions, a lengthy process that can take years, or figure out how to fill the budget hole, most likely by cutting other services or raising taxes.

The constitutional amendments were put on state ballots by progressive activists, who wanted to entrench the Medicaid program in places that had been hostile to that part of the Affordable Care Act. The idea was twofold: to get health coverage to more people, and to tether more states and their Republican lawmakers to Medicaid.

The ballot initiatives passed by a wide margin, and now these states have more at stake in the congressional debate over Medicaid. Even some conservative senators, like Josh Hawley of Missouri, are speaking out against reducing funding for the program. The Republican senators from the three states with constitutional amendments could become an unlikely part of the firewall against big cuts to Medicaid.

“Expanding Medicaid anywhere protects it everywhere, which is now what we’re seeing today,” said Kelly Hall, executive director of the Fairness Project, the nonprofit that organized the constitutional amendment campaigns. She noted that her group expected the expansions would broaden support for the program in Washington.

The exact details of any cuts are still unclear, but Republicans in Congress hope to enact a detailed plan by the end of September. A budget resolution that passed the House last month called for at least $880 billion in cuts over a decade from the committee that oversees Medicaid. If all the cuts came from Medicaid, that amount would represent an 11 percent reduction in federal Medicaid spending, and millions would most likely lose coverage. The Senate passed its own budget Saturday that included the House numbers but was less clear on the scope of its preferred spending cuts.

Lawmakers and policy analysts who favor cuts argue that states no longer pay their fair share of Medicaid’s bills. In recent years, the federal share of spending on the program has grown to more than 70 percent overall from around 60 percent. The federal government pays 90 percent of the costs for working-age adults who enroll through the expansion, a high share that the architects of Obamacare meant to ease the burden of expansion from state budgets.

Because states would become responsible for what had once been paid by the federal government, the states with constitutional amendments would have especially high financial stakes. In Missouri, Medicaid funding makes up about 35 percent of the state’s entire budget. If the federal government pulled back, the state would probably have to raise taxes or cut other parts of its budget, like education or transportation.

The last time Republicans attempted major Medicaid changes, as part of their Obamacare repeal push in 2017, some Republican governors lobbied their senators to protect the program, and several voted against the bill. In the years since, seven more Republican-led states have expanded Medicaid by ballot measure, expanding coverage to 950,000 people.

Even after passing at the ballot, Medicaid expansion still faced opposition from elected officials charged with setting up the program. The former Maine governor Paul LePage went the furthest, claiming he would go to jail rather than carry out a Medicaid expansion. (The expansion was implemented after he was replaced by a Democrat.)

That resistance got the progressive activists who organized and funded the ballot initiative campaigns looking for a way to make Medicaid expansion more ironclad. For 2020, they came up with the idea of pursuing voter referendums to enshrine participation in the program in state constitutions. They succeeded in Missouri and Oklahoma in 2020, followed by South Dakota in 2022.

Those ballot initiatives took more work, requiring more signatures to get onto the ballot. Activists decided the extra hurdle was worth it to entrench Medicaid in areas of the country that had been hostile to the program — thus giving it more protection in Washington.

The politics of the Republican Party have changed since 2017, too, shifting from Tea Party austerity toward working class populism. Hospitals have also become more dependent on Medicaid as it has expanded, and more effective at arguing this point to government officials.

“The system is much more firmly in place now than it was eight years ago,” said Brendan Buck, who was an aide for Speaker Paul Ryan during the Obamacare repeal effort in 2017 and is now a partner in a communications firm that does work for health industry clients. “These are our states. These are our voters. And I think they will hear loud and clear if this does become a real threat.”

When he was Missouri’s attorney general, Mr. Hawley led two lawsuits seeking to overturn the Affordable Care Act. But in February and again this past week, he voted with Democrats on budget amendments to protect Medicaid. Those efforts were largely ceremonial. But Republicans may need his vote to advance their larger package of tax cuts and spending reductions later this year.

“Our voters voted for it — my constituents — by a decisive margin,” Mr. Hawley said of Medicaid expansion in a recent interview, noting that a fifth of the state gets health insurance through the program.

While Mr. Hawley said he would be comfortable voting to add a work requirement to the program, he was “not going to vote for cut benefits.”

Senator Mike Rounds of South Dakota has also opposed reducing federal funding for Medicaid expansion because of the financial burden it would put on states. “That’s not a cost-cutting measure — that’s a cost transfer,” he told Politico in February.

Even many blue states that passed expansion through their legislatures will probably stop Medicaid coverage for poor adults if cuts go through. Twelve states, including Illinois and Virginia, have passed legislation that would automatically rescind the expansion if federal funding dips.

The states with constitutional amendments are already beginning to prepare for the possibility of a major budget hole. In Oklahoma, for example, federal Medicaid funding makes up almost 30 percent of the state’s entire budget.

A conservative Oklahoma think tank has suggested that the state cut other parts of Medicaid to make up the gap instead of dipping into funding for services like roads or schools.

But reducing Medicaid services alone probably wouldn’t be enough to offset the lost federal funding. There are only a handful of ways states are allowed to cut the program, such as ending coverage for prescription drugs or no longer providing insurance to postpartum women.

In South Dakota, the Legislature passed a law in February that would alter the constitution to leave the program if federal funding dropped.

The new law wouldn’t immediately pull South Dakota out of Medicaid expansion but would give the Legislature the flexibility to do so. To change the constitution, voters would also need to weigh in with a new ballot initiative, scheduled for the state’s next election in 2026 — potentially after Congress passes cuts.

“I’m worried it won’t be soon enough, but that is when our next election is,” said Tony Venhuizen, who introduced the bill in January as a member of the State Legislature. “There isn’t another way.”

Catie Edmondson contributed reporting.