A draft proposal by Speaker Nancy Pelosi would empower the federal government to negotiate lower prices for hundreds of prescription drugs, not only for Medicare but for the private market as well, injecting new urgency into Washington’s efforts to control the soaring price of pharmaceuticals.

The plan would revive an idea loathed by most congressional Republicans but long embraced by Democrats; President Trump expressed support for it during his 2016 campaign. By the time he hits the campaign trail again next year, Mr. Trump wants to persuade voters that he lowered the cost of prescription drugs — an issue that resonates with Americans of all political persuasions and a promise he has made repeatedly.

The speaker’s plan is the latest in a growing constellation of proposals. At the same time, the pharmaceutical industry is ramping up its campaign to kill them.

A potential curveball is a plan the Trump administration has been working on that would base the price that Medicare pays for some drugs that are administered by doctors, such as chemotherapy and other intravenous infusions, on what other countries, including Canada and Germany, pay for the same medications.