With Republicans set to control Washington, conservative lawmakers and policy experts who could advise the next Trump administration are discussing long-sought cuts to Medicaid, the government health program that covers roughly a fifth of all Americans and makes up about 10 percent of the federal budget.

Some of the changes are being proposed as a way to pay for a law that would extend the tax cuts from the first Trump administration, most of which benefited corporations and wealthier Americans. The policies might slash funding for Obamacare’s Medicaid expansion — which added roughly 23 million people to the program — or require that many enrollees work in order to receive benefits.

Representative Jodey Arrington of Texas, a Republican who leads the House Budget Committee, told reporters last week that he favored a “responsible and reasonable work requirement” for Medicaid.

And Senator John Cornyn, another Republican from Texas, said of Medicaid, “We ought to look at whether we’re doing it the right way.” He said he supported “block grants,” in which states get lump sums, regardless of how many people sign up for the program.

These ideas resurrect conservative proposals going back years, and have appeared in recent House Republican budget proposals and in the high-profile policy agenda known as Project 2025. Work requirements, which struggled to get off the ground in the first Trump administration, would cut federal spending by at least $100 billion over the next decade and cause 600,000 people to lose coverage, according to estimates from the Congressional Budget Office.

“If you want to avoid a debt spiral there have got to be reforms made to federal health programs,” said Brian Blase, a former Trump health policy adviser who now runs Paragon Health Institute, a conservative think tank. Mr. Blase has discussed Medicaid reform in recent years with conservative lawmakers and aides.