(CNN) President Donald Trump's legal team will go into his Senate trial on Tuesday arguing that he should never have been impeached because his conduct over Ukraine does not amount to a criminal offense.

First details of the President's counter-argument are emerging from a document the White House sent to Capitol Hill on Saturday night and in television interviews of one of his new legal advisers. Senate Republicans, who will serve as jurors, are quickly buying into his new defense.

Trump was impeached by the House last month on charges of abuse of power and obstructing Congress over his scheme to pressure Ukraine for political favors -- including the announcement of a probe into Joe Biden, a possible 2020 election opponent.

Harvard Professor Emeritus Alan Dershowitz , who has just joined Trump's legal brain trust, told CNN's "State of the Union" Sunday that he would borrow arguments made by former Supreme Court Justice Benjamin Curtis during the impeachment of President Andrew Johnson in 1868.

"He argued successfully to the Senate that criminal-like conduct is required. That argument prevailed. I will be making that argument as a lawyer on behalf of the President's defense team against impeachment," Dershowitz said.

On "This Week" on ABC, Dershowitz argued that the articles of impeachment voted on by the House did not meet the constitutional standard for the use of Congress's most grave power to censure a President.

"You have a lot of evidence, disputed evidence that could go both ways. But the vote was to impeach on abuse of power which is not within the constitutional criteria for impeachment and obstruction of justice," he said.

In Trump's response to the Senate legal summons for his trial, his lawyers argue that the first article of impeachment against him is invalid because it "alleges no crimes at all, let alone 'High Crimes and Misdemeanors,' as required by the Constitution. In fact it alleges no violation of law whatsoever."

And in an appearance on "Fox and Friends" on Monday, another of the President's newly announced legal team Robert Ray, expanded the argument.

"Never in our history has there been an impeachment of a President without even an allegation that a crime was committed and that under the circumstances, given that, that is untethered to the foundational principles that come from the Constitution itself," Ray said.

A Democratic trial brief also released over the weekend dismisses the central plank of Trump's defense -- that an indictable crime must be committed before a President can be impeached. The document says that the Founders understood the phrase "High Crimes and Misdemeanors" to mean "acts committed by public officials that inflict severe harm on the constitutional order."

House Democratic Intelligence Chairman Adam Schiff criticized the President's effective position that abuse of power -- the subject of the first article of impeachment -- is not an impeachable offense.

"The logic of that absurdist position that's being now adopted by the President is, he could give away the state of Alaska. He could withhold execution of sanctions on Russia for interfering in the last election to induce or coerce Russia to interfere in the next one," Schiff, one of the impeachment managers who will make the case against Trump, said on "This Week."

"The mere idea of this would have appalled the founders, who were worried about exactly that kind of solicitation of foreign interference in an election for a personal benefit, the danger it poses to national security," Schiff said.

"That goes to the very heart of what the framers intended to be impeachable."

Many scholars believe that the constitutional provisions for impeachment apply to presidential misconduct wider than the commission of an actual crime and encompass the abuse by a high-ranking official of a public trust that can result from them putting their own interests above the nation's.

'Abuse of power is not impeachable'

Trump's lawyers are sketching a vision of an expansive presidency and a political system offering Congress limited power to check the commander-in-chief.

Their exceedingly aggressive response to the House impeachment case also claims that the President was denied due process in the House impeachment investigation.

The response to the summons, signed by Trump's two lawyers Jay Sekulow and Pat Cipollone, is already fulfilling part of its intended purpose -- arming Republican senators with pre-trial arguments to counter a detailed Democratic case alleging gross abuse of presidential authority.

"He's been charged with abuse of power, which is not treason, which is not bribery, which is not a high crime and misdemeanor," Texas GOP Sen. John Cornyn said on CBS' "Face the Nation" on Sunday.

"So, this is the first time in history where a President has been impeached for a non-crime for events that never occurred," he said.

Georgia Sen. David Perdue, another Trump ally, picked up on the legal response's argument that the Democrats had subverted the impeachment process itself -- even though the Constitution gives the House sole power to set the procedures of the process and the President declined to send representatives to Judiciary Committee hearings.

"This has all been tried out in the media. I mean, he has not had an opportunity," Perdue told "Meet the Press" on NBC. "Remember, next week is going to be the first time America gets to hear President Trump's defense."

The legal response and the public comments of members of his legal team represents the President's most coherent push back yet against his impeachment.

Trump's defense also largely ignores the evidence piled up by the House impeachment inquiry. It implicitly argues that withholding aid in an effort to procure political favors -- in this case from Ukraine -- is well within a President's prerogative and that Congress lacks the power to investigate it.

Democrats mock new Trump defense

The President's brief is shaping fierce debate over whether Republicans will allow new witness testimony during the trial.

Senate Democratic Minority Leader Chuck Schumer said Sunday evening that if Senate Majority Leader Mitch McConnell does not call for witnesses in his proposal for trial procedures, he would force votes on the issue at the start of the trial.

"We're allowed to amend it, and ask for them. I am allowed to amend it -- and then if they say well let's wait and hear the arguments we'll want a vote after they hear the arguments as well and we will do everything we can to force votes again," Schumer said at a press conference in New York.

New revelations about Trump's scheme to go around formal diplomatic channels in Ukraine -- notably from indicted Rudy Giuliani associate Lev Parnas are putting pressure on GOP senators on the witness issue.

The dueling Democratic and Republican narratives heading into the Senate trial reflect the high political stakes even though Trump's acquittal is almost guaranteed. Democrats want the public to perceive the GOP as shielding a corrupt president in an unfair trial. Republican leaders hope to protect their vulnerable members in swing states where Trump is unpopular and are constrained by the President's stranglehold on the conservative base -- on issues like witnesses especially.

"The Senate itself is on trial, as far as I'm concerned, and the jury is the American people," Illinois Sen. Dick Durbin said on "Meet the Press," revealing the Democratic tactic of making life as uncomfortable as possible for Republican senators as the trial gets underway.

"A fair trial, everyone understands, involves evidence. Evidence would be documents and witnesses," Durbin said. "At this point, you know, the Senate is on trial. And I hope at the end of the day enough Republican senators will understand history will find you. Make certain that you make a decision that you can live with in terms of our Constitution and your own professional career."

In their own detailed filing issued over the weekend, Democrats made the case that the Senate's expected failure to convict Trump of impeachable crimes would change the presidency forever.

"His misconduct challenges the fundamental principle that Americans should decide American elections, and that a divided system of government, in which no single branch operates without the check and balance of the others, preserves the liberty we all hold dear," the Democratic brief said.