The drain on Medicaid funding would worsen over time under the bill that Senate Republicans are working to pass, with the new funding limits starting in 2021 and having the biggest impact more than a decade from now. The nonpartisan Congressional Budget Office estimated that Medicaid spending would be 26 percent lower under the Senate plan than it would be under current law in 2026 — and 35 percent lower in 2036. The office predicted that states would be forced to “eliminate optional services, restrict eligibility for enrollment or adopt some combination of those approaches.”

Under the Senate plan, states would receive a fixed annual amount for each Medicaid beneficiary, with each category of beneficiaries, like children and the disabled, getting a different base amount based on recent costs. The amount would increase every year by a formula that is expected to grow more slowly than average medical costs after 2025. Disabled children would not be subject to the spending caps.

Avalere Health, a consulting firm, estimated in a report that federal spending on individual state Medicaid programs could decline between 6 percent and 26 percent under the Republican plan by 2026. The biggest drops would be in states that expanded Medicaid, but the cuts would compound more sharply for every state in later years.

Conservatives say Medicaid spending, which consumes a major and growing portion of the federal and states’ budgets, needs to be reined in. The current system of unlimited federal matching funds, they say, has encouraged states to milk as much as they can, sometimes wastefully; capping funding, their argument goes, would make Medicaid more efficient and ensure it can continue to help the most vulnerable Americans, including people with disabilities.

“The fiscal sustainability of Medicaid is essential to making sure that those who depend on the program can know it will be there for them in the future,” Avik Roy, a conservative health care analyst, wrote last week in Forbes.