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It was not to be.

Minutes later, a group of protesters in the back of the Capitol Hill hearing room began shouting at lawmakers to “keep your greedy hands off our Medicaid.”

They drowned out the chairman’s calls for order, and Capitol Police officers ultimately removed five people — three in wheelchairs — as the dozens of lawmakers on the panel looked on. (The Capitol Police later said that officers had arrested 26 people for illegally protesting inside a congressional building.)

The disruptions were a raucous kickoff to a meeting that went all evening and was expected to continue well into Wednesday — one committee member estimated it could take as long as 28 hours — as Republicans and Democrats sparred over the plan, a key part of major legislation to enact President Trump’s domestic agenda.

It unfolded as the tax-writing House Ways and Means Committee met to consider a $2.5 trillion tax proposal that would extend Mr. Trump’s 2017 tax cuts; temporarily fulfill his campaign pledges not to tax tips or overtime pay; roll back subsidies for clean energy; and create a new type of tax-advantaged investment account for children.

Democrats on the Ways and Means Committee tried unsuccessfully to extend tax credits that have helped people buy insurance on the Obamacare marketplaces. The subsidies are scheduled to expire at the end of the year, and the Congressional Budget Office estimates that more than four million people will lose coverage as a result.

Representative Steven Horsford, Democrat of Nevada, proposed an amendment that would have made the extra funding permanent. He argued that, because Republicans were using an unconventional form of accounting in their effort to make other tax cuts permanent, they should use the same approach to keep insurance premiums affordable.

“You cannot in one breath say it’s OK to provide tax cuts for billionaires and that can be free, and not provide tax relief for working families for health care, for God’s sake,” he said.

A third panel, the House Agriculture Committee, also met Tuesday night and began considering a piece of the bill that would slash nutrition assistance to help raise money for the plan.

But the bulk of the drama on Tuesday was at the Energy and Commerce Committee. During the first hour alone, Republicans giving opening statements were interrupted repeatedly by protesters who accused them of taking health care away from vulnerable people. G.O.P. lawmakers, in turn, accused Democrats of misrepresenting the Medicaid cuts they are proposing to score political points.

Mr. Guthrie labored to keep control over the proceedings, at one point presiding over a shouting match over whether members of his panel were allowed to use the word “lying” in their remarks. (Republicans had been permitted to say that Democrats were lying about the scope of the Medicaid cuts, but Democrats were barred from saying that Mr. Trump was lying about his desire to protect the program. An informal agreement to simply avoid using the word “lie” altogether for the remainder of the session fell apart a few hours later.)

Even some Democratic senators came to take in the spectacle. Senators Cory Booker of New Jersey, Brian Schatz of Hawaii and Tina Smith of Minnesota were on hand.

That was all before lawmakers had debated a single provision of the measure. Eight hours into the hearing, the committee had yet to debate the Medicaid cuts, focusing instead on other changes in environmental and energy policy.

The bill’s proposed reductions in Medicaid coverage and its expansion under the Affordable Care Act have become a flashpoint for Democrats and an area of concern for vulnerable Republicans who are wary of the political consequences of supporting cuts to insurance programs that have become popular with Americans.

Though House Republicans shied away from a huge structural overhaul of Medicaid, their proposal would reduce federal spending by an estimated $912 billion and cause 8.6 million people to become uninsured, according to a partial analysis from the Congressional Budget Office that was circulated by Democrats on the committee. Around $700 billion in cuts would come from changes to Medicaid and the Affordable Care Act.

Republicans argued that their proposed cuts would help control rising Medicaid costs by targeting “waste, fraud and abuse” and ensuring the program’s long-term health.

“Medicaid was created to protect health care for Americans who otherwise could not support themselves, but Democrats expanded the program far beyond this core mission,” Mr. Guthrie said.

Their proposal calls for stricter paperwork requirements across the program, makes changes that affect federal funding to states and adds a work requirement to Medicaid that requires poor, childless adults to prove they are working 80 hours every month to stay enrolled.

That provision, which targets an expansion of Medicaid under the Affordable Care Act, would not kick in until January 2029, after the next presidential election.

During their opening remarks, Democrats on the committee held up matching posters with photographs of constituents they deemed the “faces of Medicaid.” The lawmakers told their stories as a way of humanizing people who rely on the program.

Representative Debbie Dingell of Michigan directly addressed a family who had traveled to Washington in the hearing, who she said needed Medicaid to care for a child with Down syndrome. Representative Marc Veasey of Texas held his phone up to the microphone, inviting a constituent to speak about how Medicaid affected her. Mr. Guthrie ruled that out of order.

Some of the people being highlighted were not at risk of losing coverage under the Republican proposal. And Democrats frequently claimed that the Republican plan would cause 13.7 million Americans to become uninsured, inflating the bill’s effects on coverage by about five million people.

Pointing to these discrepancies, Republican lawmakers accused Democrats of dishonest politicking.

“Not a single person on these posters is going to be affected,” Representative Kat Cammack of Florida said.

“It’s unfortunate that people are so enraged by misinformation,” Representative Gary Palmer, Republican of Alabama, said, referring to a woman who was taken from the room by the police after she shouted that she was H.I.V. positive and that the Medicaid cuts “will kill me.”

As the hearing started, the hallway outside was packed with protesters, many of them wearing shirts or bearing signs that read “Hands Off Medicaid.” Others wore shirts reading “Fight for Planned Parenthood.” The organization is targeted by a provision in the bill that would block Medicaid from funding health providers that also offer abortion services.

“Hopefully, everyone understands that these demonstrations — people feel very strongly,” Representative Frank Pallone Jr., the top Democrat on the committee, said. “Because they know they’re losing their health care.”

Catie Edmondson contributed reporting.