Eight years ago, just before the Iowa caucuses, Donald J. Trump crowed about his invulnerability.

“I could stand in the middle of Fifth Avenue and shoot somebody, and I wouldn’t lose any voters, OK?” he said. “It’s, like, incredible.”

On Tuesday, at a federal appeals court argument held the week before this year’s caucuses, a lawyer for Mr. Trump said that the Constitution basically states the same thing.

It took a few questions from Judge Florence Y. Pan to pin down the lawyer, D. John Sauer. But in the end he made the jaw-dropping claim that former presidents are absolutely immune from prosecution even for murders they ordered while in office.

“I asked you a yes-or-no question,” Judge Pan said. “Could a president who ordered SEAL Team 6 to assassinate a political rival, who was not impeached, would he be subject to criminal prosecution?”

Mr. Sauer said his answer was a “qualified yes,” by which he meant no. He explained that prosecution would only be permitted if the president were first impeached by the House and convicted by the Senate.

Impeachments of presidents are rare: There have been four in the history of the Republic, two of them of Mr. Trump. The number of convictions, which require a two-thirds majority of the Senate: zero.

A member of Congress might be reluctant, in any event, to vote against a president prepared to order the military to murder his opponents.

Mr. Sauer’s answer instantly entered the annals of candid concessions that helped doom an argument. It was reminiscent of a government lawyer’s statement, at the first argument in the Citizens United campaign finance case, in 2009, that Congress could in theory ban books urging the election of political candidates.

“That’s pretty incredible,” Justice Samuel A. Alito Jr. said at the time. When the case was reargued, Solicitor General Elena Kagan, now a member of the Supreme Court, modified the government’s position but lost anyway, by a 5-to-4 vote.

Mr. Sauer’s statement also called to mind a more direct echo, from a 2019 federal appeals court argument over whether Mr. Trump could block state prosecutors from obtaining his tax and business records. He maintained that he was immune not only from prosecution but also from criminal investigation so long as he was president.

At that time, Judge Denny Chin pressed William S. Consovoy, a lawyer for Mr. Trump, asking about his client’s statement that he could shoot someone on Fifth Avenue without losing political support.

“Local authorities couldn’t investigate?” Judge Chin asked, adding: “Nothing could be done? That’s your position?”

“That is correct,” said Mr. Consovoy, who died last year. “That is correct.”

This headline followed: “If Trump Shoots Someone on 5th Ave., Does He Have Immunity? His Lawyer Says Yes.”

Mr. Trump’s general strategy is not new. He has long sought expansive immunity, and he has frequently invoked impeachment as the primary remedy for presidential misconduct.

But Mr. Sauer’s reading on Tuesday of what lawyers call the impeachment judgment clause did not impress legal scholars.

The provision says: “Judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States: But the party convicted shall nevertheless be liable and subject to indictment, trial, judgment and punishment, according to law.”

It is plain that “the party convicted” in the Senate can still face criminal prosecution. But Mr. Sauer argued that the clause implied two other things: that conviction in the Senate is always required before a criminal prosecution and that acquittal in the Senate bars such prosecution.

Abner S. Greene, a law professor at Fordham University, said that “the impeachment arguments are sure losers — both that the president may be criminally prosecuted only if impeached and convicted, and that the president may not be criminally prosecuted if impeached and not convicted.”

Mr. Trump was acquitted at his second impeachment trial when only 57 senators voted against him, 10 shy of the two-thirds majority needed to convict.

There are reasons to question whether that acquittal bars criminal prosecution. First, Mr. Trump was impeached for inciting insurrection, a claim notably absent from the federal indictment in the election-interference case.

Second, many senators voted to acquit Mr. Trump at the impeachment trial at least in part because he was no longer in office and so, they said, was not subject to the Senate’s jurisdiction.

Third, Mr. Trump’s own lawyers argued at the impeachment trial that the proper response to their client’s conduct was criminal prosecution.

Given Mr. Sauer’s answer on assassination and the gaps in his argument grounded in the impeachment judgment clause, Mr. Trump is likely to lose before the three-judge panel. But he has achieved a significant interim victory. Proceedings in the trial court have been suspended during the appeal and the scheduled start of the trial, on March 4, may slip.

Should Mr. Trump lose before the three-judge panel, he may ask the full appeals court, the U.S. Court of Appeals for the District of Columbia Circuit, to rehear the case. It is unlikely to agree to do so, but ruling on the request could take time.

After that, Mr. Trump would very likely ask the U.S. Supreme Court to hear the case. Last month, the justices turned down an unusual request from Jack Smith, the special counsel, to leapfrog the appeals court and consider the matter immediately.

But that is no reason to think the Supreme Court will not want to have the last word on a question as consequential as the scope of presidential immunity. Even if the court moves very quickly — as it so far has on the separate question of whether Mr. Trump is eligible to hold office under the 14th Amendment — it could take several weeks to render a decision.

Time, in other words, is Mr. Trump’s friend. If he can defer the case beyond the election in November and win at the polls, he could try to pardon himself or instruct the Justice Department to drop the case against him. Such moves, in turn, could bring the matter full circle — by prompting calls for a third impeachment.

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