Donald Trump’s Republican congressional allies are throwing up different defenses against impeachment and hoping that something may sell. They say that he didn’t seek a corrupt political bargain with Ukraine, but that if he did, he failed, and the mere attempt is not impeachable. Or that it is not clear that he did it, because the evidence against him is unreliable “hearsay.”

It’s all been very confusing. But the larger story — the crucial constitutional story — is not the incoherence of the president’s defense. It is more that he and his party are exposing limits of impeachment as a response to the presidency of a demagogue.

The founders feared the demagogue, who figures prominently in the Federalist Papers as the politician who, possessing “perverted ambition,” pursues relentless self-aggrandizement “by the confusions of their country.” The last of the papers, Federalist No. 85, linked demagogy to its threat to the constitutional order — to the “despotism” that may be expected from the “victorious demagogue.” This “despotism” is achieved through systematic lying to the public, vilification of the opposition and, as James Fenimore Cooper wrote in an essay on demagogues, a claimed right to disregard “the Constitution and the laws” in pursuing what the demagogue judges to be the “interests of the people.”

Should the demagogue succeed in winning the presidency, impeachment in theory provides the fail-safe protection. And yet the demagogue’s political tool kit, it turns out, may be his most effective defense. It is a constitutional paradox: The very behaviors that necessitate impeachment supply the means for the demagogue to escape it.

As the self-proclaimed embodiment of the American popular will, the demagogue portrays impeachment deliberations as necessarily a threat to democracy, a facade for powerful interests arrayed against the people that only he represents. Critics and congressional opponents are traitors. Norms and standing institutional interests are fraudulent.

President Trump has made full use of the demagogic playbook. He has refused all cooperation with the House. He lies repeatedly about the facts, holds public rallies to spread these falsehoods and attacks the credibility, motives and even patriotism of witnesses. His mode of “argument” is purely assaultive. This is the crux of the Trump defense, and not an argument built on facts in support of a constitutional theory of the case.

Of course, all the presidents who have faced impeachment mounted a political defense, to go with their legal and constitutional case. And it is not unusual that they — and, even more vociferously, their allies — will attack the process as a means of undoing an election.

The difference in Mr. Trump’s case is not merely one of degree. Richard Nixon despised his opposition, convinced of their bad faith and implacable hatred for him. But it is hard to imagine Mr. Trump choosing (and actually meaning) these words to conclude, as Nixon did, a letter to the chair of Judiciary Committee: “[If] the committee desires further information from me … I stand ready to answer, under oath, pertinent written interrogatories, and to be interviewed under oath by you and the ranking minority member at the White House.”

Mr. Trump has instead described Adam Schiff, the chairman of the Intelligence Committee, as a “corrupt” politician who shares with other “human scum” the objective of running the “most unfair hearings in American history.”

These remarks are not merely one more instance of Mr. Trump’s failure to curb his impulses. This is his constitutional defense strategy. Mr. Trump’s White House counsel, informing the House of the president’s refusal to cooperate, declared that the impeachment process is unconstitutional and invalid — a “naked political strategy” — and advised that the president would not participate. It matters that the president’s lawyer, in a formal communication with the House, used rhetoric that might have been expected from the hardest-core political supporters. Once again, contrasts with past impeachments are illuminating. Bill Clinton’s White House counsel Charles Ruff testified before the House Judiciary Committee, pledging to “assist you in performing your constitutional duties.”

The demagogue may be boundlessly confident in his own skills and force of political personality, but he cannot succeed on those alone. He can thrive only in political conditions conducive to the effective practice of these dark arts, such as widespread distrust of institutions, a polarized polity and a fractured media environment in which it is possible to construct alternative pictures of social realities. Weak political parties now fall quickly into line with a demagogue who can bring intense pressure to bear on party officials and officeholders through his hold on “the base.” As we have seen with Mr. Trump, the demagogue can bully his party into being an instrument of his will, silencing or driving out dissenters. Republican officeholders know that Mr. Trump can take to Twitter or to Fox News or to the podium at rallies — or all of the above — to excoriate them for a weak will or disloyalty.

This is how the Republican Party has become Mr. Trump’s party. It is also why that party will not conceive of its role in impeachment as entailing a constitutional responsibility independent of the president’s political and personal interests. It has come to see those interests as indistinguishable from its own. In this way the constitutional defense of the case against Mr. Trump and the defense of his own interests become one and the same. As another fabled demagogue, Huey Long of Louisiana, famously announced: “I’m the Constitution around here now.”

The implications for the constitutional impeachment process are dire. Until Mr. Trump, modern impeachment has ended with some generally positive assessment of its legacy. Nixon’s resignation appeared to indicate that serious charges could bring the parties together in defense of the rule of law. “The system worked” was a popular refrain, even if this was a somewhat idealized and oversimplified version of events. The Clinton impeachment suggested that the standards for an impeachable offense required a distinction between public misconduct and private morality, and Congress reclaimed its responsibility for impeachment from an independent counsel statute that was allowed to lapse.

The Trump impeachment is headed toward a very different summation. A demagogue can claim that Congress has forfeited the right to recognition of its impeachment power, then proceed to unleash a barrage of falsehoods and personal attacks to confuse the public, cow legislators and intimidate witnesses. So long as the demagogue’s party controls one of the two chambers of Congress, this strategy seems a sure bet.

When this is all over, we will not hear warm bipartisan praise for how “the system worked.” The lesson will be that, in the politics of the time, a demagogue who gets into the Oval Office is hard to get out.

Bob Bauer is a professor of practice and distinguished scholar in residence at New York University School of Law and served as a White House counsel under President Barack Obama.