“Trump is doing this not for national security reasons but to impede an investigation into himself and his associates, and he’s staking a far more sweeping claim to power than even other presidents by saying he can use the Justice Department for whatever he wants,” Mr. Kris said.

He added: “They are saying not just that the president is above the law, but in effect that he is the law — that he is the personification of justice and cannot obstruct himself. That is very stark and not very persuasive.”

The constitutional theory Mr. Trump’s team has put forward is not his first line of defense. They also have mustered factual claims, denying wrongdoing and arguing that as a technical matter, a particular obstruction statute did not apply to his actions. (The memo, however, appeared to be focused on the wrong statute, rendering the statutory arguments beside the point.)

But the Trump team is invoking its aggressive constitutional theory to backstop its other arguments. Even though Congress has made it a crime to impede a pending or potential grand-jury investigation or trial with corrupt intentions, they said, that statute cannot be applied to Mr. Trump, no matter what the evidence shows about his actions and intentions.

Both Nixon and President Bill Clinton were accused of obstruction of justice by lawmakers as part of impeachment proceedings, drawing on evidence brought to light by prosecutors who, rather than charging them with crimes, sent reports to the House Judiciary Committee for impeachment consideration. But the actions those presidents were accused of — like witness tampering or suborning perjury — were not an exercise of their official powers as president.

The novel issue raised by the investigation into Mr. Trump — assuming Mr. Mueller has not uncovered evidence of other obstructive actions that is not yet public — is whether Congress can make it a crime for him to use his power over the law enforcement system with a corrupt purpose, even if it would otherwise be lawful for him to take such steps.

“Put simply,” Mr. Kasowitz wrote last June, “the Constitution leaves no question that the president has exclusive authority over the ultimate conduct and disposition of all criminal investigations and over those executive branch officials responsible for conducting those investigations.”