The Jan. 6 committee’s hearing on Thursday, which documented the relentless but unsuccessful campaign by President Donald J. Trump to pressure Vice President Mike Pence into helping him to reverse his defeat in the 2020 election, swerved wildly at times between wonky discussions of constitutional law and unsettling images of the threats and violence that Mr. Trump’s attacks on Mr. Pence inspired.But at the heart of the committee’s presentation was a straightforward narrative.Weeks before the mob attack on the Capitol, Mr. Trump joined forces with a law professor named John Eastman, who was espousing a theory that Mr. Pence, in his role as president of the Senate, had the power to alter the outcome of the election — or at least to delay certification of Mr. Trump’s defeat.Armed with this dubious legal cudgel, and with his other avenues for retaining power closing off, Mr. Trump pushed and pushed at Mr. Pence, including publicly on Jan. 6, helping to rile up his supporters and trigger the riot at the Capitol.Mr. Pence — backed by his own advisers and other legal experts — resisted Mr. Trump from the moment the idea came up.Here are four takeaways from Thursday’s hearing.Even Eastman doubted his plan’s legality, and he let Trump know that.The panel displayed on Thursday an image of the handwritten notes of Greg Jacob, attorney for Vice President Mike Pence, from a meeting with John Eastman.Doug Mills/The New York TimesMr. Trump went ahead with the pressure campaign on Mr. Pence even though Mr. Eastman, a former clerk to Justice Clarence Thomas and a law professor at Chapman University, was less than certain at times about the legality and political viability of his own plan.The committee, for example, introduced an email that Mr. Eastman had written in the early stages of the scheme, in which he said that the idea of having lawmakers in pro-Trump states draft alternate slates of electors to give Mr. Pence a reason for disputing the results was “dead on arrival in Congress.”Mr. Eastman also admitted in a private conversation with Mr. Pence’s top lawyer, Greg Jacob, that if the Supreme Court ever had to rule on the legality of a vice president deciding the results of an election on his own, the court would unanimously vote to toss the matter, Mr. Jacob testified.But more important, Mr. Jacob told the committee in a videotaped deposition — snippets of which were played during the hearing — that Mr. Eastman had admitted in Mr. Trump’s presence that the plan to pressure Mr. Pence violated an 1887 law known as the Electoral Count Act. According to Mr. Jacob, Mr. Eastman acknowledged the illegality of the scheme in front of Mr. Trump on Jan. 4, 2021, just two days before Mr. Pence was to oversee the certification of the election.That crucial admission by Mr. Eastman was highlighted by Representative Liz Cheney, Republican of Wyoming and the committee’s vice chairwoman, who has long suggested that Mr. Trump could be charged with a federal crime for the role he played in obstructing the certification of the vote count on Jan. 6.The Themes of the Jan. 6 House Committee HearingsMaking a Case Against Trump: The committee appears to be laying out a road map for prosecutors to indict former President Donald J. Trump. But the path to any trial is uncertain.Day One: During the first hearing, the panel presented a gripping story with a sprawling cast of characters, but only three main players: Mr. Trump, the Proud Boys and a Capitol Police officer.Day Two: In its second hearing, the committee assembled an account of how Mr. Trump’s advisers urged him not to declare victory on election night in 2020, but instead he listened to Rudolph W. Giuliani.A Striking Contrast: Many Trump officials have told the committee that they tried to dissuade the former president from his bid to overturn the election. But at the time, their words were far different in public.Fund-Raising Tactics: The Jan. 6 panel has raised questions about Mr. Trump’s aggressive solicitations, accusing him of misleading donors with election fraud claims.If prosecutors can prove that both Mr. Trump and Mr. Eastman were aware in advance that the scheme to pressure Mr. Pence would violate the law, it could be an important piece of evidence suggesting intent, should the Justice Department decide to pursue a criminal case against either of them.Both Ms. Cheney and a colleague on the committee, Representative Pete Aguilar, Democrat of California, mentioned that a federal judge had already ruled in a related civil suit that Mr. Trump and Mr. Eastman most likely conspired together to obstruct the certification of the election and to commit fraud against the United States.In his ruling from March, Judge David O. Carter wrote that “the illegality of the plan was obvious,” calling it a “coup in search of a legal theory.”Mr. Eastman was apparently sufficiently worried about being prosecuted for his role that he inquired a few days after Jan. 6 about getting a pardon before Mr. Trump left office.Pence never wavered on rebuffing Trump.Vice President Mike Pence, with House Speaker Nancy Pelosi, certifying the results of the 2020 election on Jan. 6, 2021.Erin Schaff/The New York TimesIf there was one thing the committee’s hearing made clear, it was that Mr. Pence, despite his history of loyalty to Mr. Trump, never believed he had the power to decide the election — and almost no one else in Mr. Trump’s orbit did, either.According to Mr. Jacob, Mr. Pence’s “first instinct” was to reject the notion out of hand, undercutting assertions by Mr. Trump’s allies at the time that he was open to the idea. Mr. Jacob told the committee that even during his first meeting with Mr. Pence about Mr. Eastman’s plan, the vice president was horrified, saying he did not believe that the founders who “abhorred concentrated power” would have ever agreed that one person — especially one who had an interest in the outcome — could have exercised sole discretion over an election.Mr. Pence, it turned out, had wide support both inside and outside the White House. The committee, in its presentation, offered up a lengthy list of aides and advisers who seemed to disagree with Mr. Trump and Mr. Eastman.In a recorded deposition, Marc Short, Mr. Pence’s chief of staff, said that Mark Meadows, Mr. Trump’s own chief of staff, agreed that the vice president did not have a broad or decisive role to play in determining election results.Another top Trump aide, Jason Miller, in his own recorded deposition, told the committee that Pat Cipollone, Mr. Trump’s White House counsel, thought Mr. Eastman’s plan was “nutty.” He added that Sean Hannity, the very pro-Trump Fox News host, felt that Mr. Pence had done the “right thing” by rebuffing it.Even Mr. Trump’s personal lawyer, Rudolph W. Giuliani, seemed to doubt Mr. Eastman’s legal theory, according to Eric Herschmann, a former top White House lawyer. But, as Mr. Herschmann noted in a recorded deposition, that did not stop Mr. Giuliani from publicly promoting Mr. Eastman’s plan on Jan. 6.There was no legal underpinning to the Eastman plan.J. Michael Luttig, a former federal appeals court judge, speaking during Thursday’s hearing.Doug Mills/The New York TimesAt times, the hearing sounded not unlike like a law school seminar on election procedure, with highly technical discussions of how the vice president’s role on Jan. 6 fit into the 12th Amendment and the Electoral Count Act.Leading those discussions was J. Michael Luttig, a former federal appeals court judge, revered by conservatives. On the morning before the Capitol attack, Judge Luttig posted a thread of messages on Twitter asserting that Mr. Pence had no power to use his own discretion in deciding the election.“The only responsibility and power of the Vice President under the Constitution is to faithfully count the electoral college votes as they have been cast,” Judge Luttig wrote.He added: “The Constitution does not empower the vice president to alter in any way the votes that have been cast, either by rejecting certain of them or otherwise.”In his testimony on Thursday, Judge Luttig denounced Mr. Eastman’s plan as “constitutional mischief,” adding that if Mr. Pence had gone along with it, it would have “plunged America into what I believe would have been tantamount to a revolution within a constitutional crisis in America.”The pressure campaign helped trigger the violence.Supporters of President Donald J. Trump storming the Capitol on Jan. 6, 2021.Jason Andrew for The New York TimesMr. Trump’s public calls for Mr. Pence to carry out Mr. Eastman’s plan raised expectations among his supporters that the vice president would do so — and ignited fury when he did not.Mr. Short, Mr. Pence’s chief of staff, had grown sufficiently concerned about the potential for Trump supporters to turn against the vice president that he alerted the Secret Service on Jan. 5.Mr. Pence continued to rebuff Mr. Trump even after a call from the president on the morning of Jan. 6 in which Mr. Trump called him a “wimp” and worse, according to testimony gathered by the committee.At 2:24 p.m. on Jan. 6, Mr. Trump sent out a tweet that said, “Mike Pence didn’t have the courage to do what should have been done.”One Trump aide told the committee that it felt at the time like Mr. Trump was “pouring gasoline on the fire.” Immediately, the committee said, there was a noticeable surge in the crowds both inside and outside the Capitol, some of whom began to chant, “Hang Mike Pence!”Mr. Pence was evacuated from his ceremonial office in the Senate and taken to a secure location, barely escaping the angry mob that breached the building. When Mr. Aguilar told Mr. Jacob, who had been with Mr. Pence in the Capitol that day, that members of the crowd had been only 40 feet from them, he seemed unnerved.“I could hear the din of the rioters in the building while we moved,” Mr. Jacob said. “But I don’t think I was aware that they were as close as that.” More