WASHINGTON — President Trump and his lawyers seem ready to wage legal war on  special counsel Robert Mueller if they deem it necessary, asserting immense executive powers that could essentially make the president immune from investigation.

In a January memo to Mueller now made public, Trump's lawyers at the time made sweeping claims that suggested Mueller's investigation may be improper and could be terminated by the president at any time.

Challenging a key facet of Mueller's probe, whether or not Trump sought to obstruct justice and cripple the Russia investigation, the memo argued that a sitting president can't obstruct justice because he is the nation's top law enforcement officer, and therefore couldn't obstruct himself.

While Trump attorney Rudy Giuliani said the legal team continues to cooperate with Mueller, critics said the memo claims powers that no president should have.

"Again and again, in different ways, it makes the point that Trump is above the law," said Norman Eisen, an ethics lawyer and senior fellow in governance studies with The Brookings Institution. "But no American is above the law, and he is going to find that out."

In Sunday show interviews, Giuliani seemed to question some of the memo's assertions — "I probably would've organized it differently," he told NBC's Meet The Press — but added that these legal questions are academic in nature and should not come into play in this case.

"We can win it on the facts," Giuliani told NBC, saying Trump did not collude with the Russians during the 2016 election and did not obstruct justice. "We don't have to get to the whole big constitutional argument which will take a year to resolve."

Analysts said the constitutional issues raised in the memo would probably have to be resolved by the Supreme Court, a confrontation that could be triggered by any number of imminent actions.

Among them:

► If Mueller subpoenas Trump for his testimony in the Russia case.

► If Mueller seeks to indict Trump over claims the president sought to obstruct justice in the investigation.

► If Trump  tries to shut down the investigation, either by having Mueller dismissed or pardoning targets of the probe like former associates Paul Manafort, Rick Gates, and Michael Flynn — or even pardoning himself.

Questions about the legal status and rights of sitting presidents are as old as the institution itself. From the Thomas Jefferson administration's treason prosecution of ex-Vice President Aaron Burr to Watergate to the saga of Ken Starr and Bill Clinton, attorneys have disagreed about the relationships between presidents and the legal system.

Attorneys with a robust view of executive power have claimed that, constitutionally, sitting presidents cannot be indicted. The remedy for presidential wrongdoing, they say, is impeachment and trial by Congress, or indictment after a president leaves office.

These same attorneys apply the same logic to the question of whether a president can be subpoenaed, saying prosecutors lack the constitutional authority to compel any presidential appearance that would interfere with the chief executive's duties.

Eisen, among others, disputes these claims, and argues that presidents can be subpoenaed and even indicted.

The subpoena question may be more pressing.

For months, Mueller and his attorneys have negotiated with the president's lawyers about testimony from Trump. While arguing for limits on time and the scope of questions for Trump, Giuliani said Sunday that at this point he would lean against having Trump testify.

Trump's team has also argued that they have supplied reams of documents to Mueller that answer his questions, rendering Trump's testimony unnecessary.

Given the impasse, Giuliani and other presidential lawyers have said Mueller at some point may be pursue a subpoena of Trump.

Mueller and his prosecutors are investigating  links between Trump's 2016 presidential campaign and Russian efforts to influence the race by hacking Democrats and pushing fake news about Democratic candidate Hillary Clinton.

The January memo, however, deals mainly with another aspect of Mueller's investigation: Whether or not Trump sought to obstruct justice in the Russia investigation by various actions, including the 2017 firing of then-FBI director James Comey.

The president's lawyers, citing Trump's "position as the chief law enforcement officer," said in their letter to Mueller that his actions "could neither constitutionally nor legally constitute obstruction because that would amount to him obstructing himself."

They added that Trump "could, if he wished, terminate the inquiry, or even exercise his power to pardon if he so desired."

Even some Trump backers balked at that defense. "It’s an outrageous claim, it’s wrong," said Chris Christie, the former New Jersey and U.S. attorney, speaking on ABC's This Week.

Christie also said that Trump would never pardon himself because that would lead to impeachment. And he added that Mueller's prosecutors have not proven they are entitled to "the extraordinary step of subpoenaing the president."

Former U.S. Attorney Preet Bharara, removed by Trump in early 2017, told CNN that the Trump legal memo "is overly expansive and overly broad." He added that the final decisions on these legal questions would, ultimately, not be made by either Trump or Mueller.

"It will be a court or it will be Congress," he said.