House Republicans hunting for ways to pay for President Trump’s tax cuts have called for cutting the federal government’s share of Medicaid spending, including a proposal that would effectively gut the Affordable Care Act’s 2014 expansion of the program.

Cutting Medicaid spending, which is central to the budget bill that House Republicans may bring to a vote on Tuesday, could result in millions of Americans across the country losing health coverage unless states decide to play a bigger role in its funding.

Republicans are considering lowering the 90 percent share that the federal government is required to pay to states that enroll participants in the expansion. The change could generate $560 billion in savings over a decade, money that Republicans want to use toward extending Mr. Trump’s 2017 tax cuts, which are set to expire at the end of 2025. Extending the tax cuts is expected to cost $4.5 trillion, meaning Republicans will have to find savings beyond Medicaid from a long menu of options.

A move to lower federal spending on the Medicaid expansion population could effectively gut the program. Around 10 states that have expanded their programs have so-called trigger laws that reverse the Medicaid expansion if the federal government decreases funding for the population.

The change could leave the 40 states that participate in the Obamacare program with a difficult set of choices. They could shoulder the extra costs to preserve Medicaid coverage for millions, make cuts to coverage or look for cuts from other large government programs to offset the reduction in federal funds.

Medicaid, which covers more than 70 million people, is the largest health insurance program in the nation, and the largest single source of funding for states. More than 21 million adults who were not eligible for Medicaid under pre-expansion guidelines received coverage last year. The program had previously restricted enrollment primarily to those who were pregnant, disabled or elderly.