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.”

For nearly six years, Speaker Paul D. Ryan has championed the new approach, denounced by Democrats as “voucherizing” Medicare. Representative Tom Price of Georgia, the House Budget Committee chairman and a leading candidate to be Mr. Trump’s secretary of health and human services, has also embraced the idea, known as premium support.

And Democrats are relishing the fight and preparing to defend the program, which was created in 1965 as part of Lyndon B. Johnson’s Great Society. They believe that if Mr. Trump chooses to do battle over Medicare, he would squander political capital, as President George W. Bush did with an effort to add private investment accounts to Social Security after his re-election in 2004.

Democrats will “stand firmly and unified” against Mr. Ryan if he tries to “shatter the sacred guarantee that has protected generations of seniors,” said Representative Nancy Pelosi of California, the Democratic leader.

Republicans have pressed for premium support since Mr. Ryan first included it in a budget blueprint in 2011. As he envisions it, Medicare beneficiaries would buy health insurance from one of a number of competing plans. The traditional fee-for-service Medicare program would compete directly with plans offered by private insurers like Humana, UnitedHealth Group and Blue Cross Blue Shield.