(CNN) President Donald Trump has decried the impeachment inquiry as a hoax and a scam run by Democratic "maniacs," but he now faces a critical choice: whether to legitimize the proceedings by allowing his lawyers to participate or refuse to take part in an inquiry he says is a sham.

The White House has been tight-lipped as it weighs the risks and potential reward of intervening in the House proceedings. House Judiciary Chairman Jerrold Nadler , the New York Democrat who will oversee the next phase of the impeachment inquiry inhearings that begin next week, told the White House on Friday that it must give a definitive answer on whether it will participate by 5 p.m. on December 6.

Reminding the President of the stakes, Nadler wrote in his Friday letter that the House Intelligence Committee is preparing its report that will describe "'a months-long effort in which President Trump again sought foreign interference in our elections for his personal and political benefit at the expense of our national interest'" and engaged in "an unprecedented campaign of obstruction in an effort to prevent the Committees from obtaining documentary evidence and testimony."

That report from the House Intelligence Committee is due as early as next week -- a chance for Democrats to make a cogent case against the President after weeks of testimony and document collection.

Nadler has offered the White House the chance to defend the President's conduct head on. It could attempt to sway public opinion by questioning witnesses, introducing its own witnesses -- if approved by the chairman, Democratic Rep. Adam Schiff of California -- and giving a concluding presentation that would offer Americans a succinct argument for Trump's side.

That opportunity to shape the narrative is especially significant because the country is so divided on the question of impeachment. The latest CNN poll found that 50% of Americans say the President should be impeached or removed from office, a number that remains unchanged from October, despite the weeks-long attempt by Democrats to present an airtight case of presidential wrongdoing.

Beneath those static topline numbers, however, a stunning 61% of women favored impeachment and removal of the President, compared with 40% of men. Presenting a coherent narrative about why Democrats are wrong during the upcoming impeachment proceedings could be critical for Trump if he wants to win back support of some of those women. (In 2016, Hillary Clinton beat Trump among women by 54% to 41%).

Women will compose a majority of the electorate next year, and the 2018 midterm election results showed that he is particularly struggling with women who live in the suburban districts that have been key battlegrounds in swing states and districts.

A coordinated White House strategy could also be more effective than the scattershot approach of Republican members of Congress, some of whom did their best to confuse the public during the Intelligence Committee hearings by raising debunked conspiracy theories and pushing the unfounded allegation that Ukraine had interfered in US elections, rather than Russia.

Republican pushback

Trump and his Republican colleagues in the House have complained vociferously about the House Intelligence Committee rules because they were excluded from those hearings. Before the hearings began, Trump tweeted : "It was just explained to me that for next weeks Fake Hearing (trial) in the House, as they interview Never Trumpers and others, I get NO LAWYER & NO DUE PROCESS. It is a Pelosi, Schiff, Scam against the Republican Party and me. This Witch Hunt should not be allowed to proceed!"

In an Oct. 8 letter to House Democratic leaders, the President's Counsel Pat Cipollone charged that they had designed their inquiry in a way that violates fundamental fairness and constitutionally mandated due process.

"You have denied the President the right to cross-examine witnesses, to call witnesses, to receive transcripts of testimony, to have access to evidence, to have counsel present, and many other basic rights guaranteed to all Americans."

White House lawyers could potentially offer Americans alternative theories for the President's pressure campaign on Ukraine. They could bring in their own witnesses to better explain why nearly $400 million in aid to Ukraine was withheld; and they could create enough doubt about the President's intentions to give a few swing-district Democrats pause before the full House votes on impeachment.

But they also would be playing that game under Democratic rules. Already the timing of the hearings conflicts with the President's schedule. One administration official told CNN's Jim Acosta on Friday not to expect Trump to participate in Wednesday's House Judiciary hearing since the commander in chief will be in London that day attending the NATO summit.

"Kind of hard when Nadler scheduled his hearing when the President is in London," the official told Acosta. "He [Nadler] has the audacity to ask whether the President will attend."

Overall the White House has not decided whether to have its attorneys at the hearing: "The letter is being reviewed and options are under consideration," the official told Acosta on Friday.

Using his bully pulpit and his Twitter account, Trump has succeeded in convincing most Republicans that the Democrats have overreached in their zealous pursuit of criminality by the President.

Public opinion barely budges

Even after a tremendous effort by the Democrats to convince Americans that Trump abused his power in pursuit of a political favor, the President's approval numbers are steady at 42%, and CNN's new poll found that only 10% of Republicans favor impeachment and removal (up from 6% in October).

Trump adopted a new line of defense this week to try to distance himself from maneuverings in Ukraine by telling conservative talk radio host Bill O'Reilly that he had no idea what his personal lawyer Rudy Giuliani was doing in Ukraine.

Other members of Trump's team, including Ambassador to the European Union Gordon Sondland , have testified that Giuliani was the point man arranging a quid pro quo of a White House meeting with Trump for Ukraine's President in exchange for the Ukrainian President publicly announcing an investigation into Joe and Hunter Biden.

There is another compelling reason why Trump and his lawyers might skip the House Judiciary proceedings, and that is because if the House impeaches him, the trial will then start in the Senate -- which is friendlier territory.

Once the inquiry moves to the Senate, Majority Leader Mitch McConnell, a Kentucky Republican, will be steering the process, giving the White House more control.

Last week, McConnell's deputies -- including Mike Lee of Utah, John Kennedy of Louisiana, Lindsey Graham of South Carolina, Tom Cotton of Arkansas and Ted Cruz of Texas -- met with Cipollone to begin discussing the framework of the trial if the House impeaches Trump, which it is expected to do by Dec. 25.

In that early meeting, a source told CNN, the leaders talked about allowing Democrats to lay out their case over a two-week period before Republicans make a move to dismiss it. But those talks are still in early days. Moreover, McConnell and Minority Leader Chuck Schumer, a New York Democrat, are expected to attempt to negotiate a bipartisan resolution setting rules and procedures for the Senate trial.

It's hard to know what that trial would look like, but the White House clearly may look more favorably on an arena where it could lay out its case without being forced to abide by the enemy's rules.