Republicans worried about losing their slim House majority next year are struggling with how to achieve Medicaid savings as even more Americans rely on the program.

After a 26-and-a-half-hour markup, Republicans on Wednesday advanced the health care section of the GOP’s sweeping tax bill that would slash Medicaid spending by hundreds of billions of dollars.

G.O.P. lawmakers from swing districts face tough votes as soon as next week, when key House panels are scheduled to consider legislation that would cut popular programs to pay for President Trump’s agenda.