WASHINGTON — Donald J. Trump once declared that campaigning for “substantial” changes to Medicare would be a political death wish.

But with Election Day behind them, emboldened House Republicans say they will move forward on a years-old effort to shift Medicare away from its open-ended commitment to pay for medical services and toward a fixed government contribution for each beneficiary.

The idea rarely came up during Mr. Trump’s march toward the White House, but a battle over the future of Medicare could roil Washington during his first year in office, whether he wants it or not.

“Let me say unequivocally to you now: I have fought to protect Medicare for this generation and for future generations,” Senator Joe Donnelly of Indiana, a Democrat running for re-election in 2018, said this week in a video message to constituents. “I have opposed efforts to privatize Medicare in the past, and I will oppose any effort to privatize Medicare or turn it into a voucher program in the future.”