“Now, maybe it’s not him. But if it’s him, you guys ought to release the information,” the president added.

Trump made his comments on the same day that top Democrats vowed to begin disclosing key details of their investigation into him. The competing messages, coming amid new polls that show a sharp increase in public support for impeachment, signaled the high stakes of trying to control the narrative as the House begins a far more contentious phase of its inquiry.

The whistleblower first called attention to the July 25 call between Trump and President Volodymyr Zelensky of Ukraine that has since led to a key question about a quid pro quo: Did the administration make military aid to Ukraine contingent on the country’s investigating former Vice President Joe Biden, a political rival of Trump’s, and his son Hunter?

A string of witnesses in the impeachment inquiry have corroborated the whistleblower’s account in congressional depositions over the past few weeks. Trump and his allies have denied that there was a quid pro quo and said there was nothing wrong in asking for an investigation into the Biden family.

Some Republican lawmakers and conservative publications have named a purported whistleblower or asserted theories about the person’s identity. The whistleblower’s lawyers released a statement on Thursday neither confirming nor denying their client’s identity but warning of the danger that comes with disclosure.

“Any physical harm the individual and/or their family suffers as a result of disclosure means that the individuals and publications reporting such names will be personally liable for that harm,” they wrote. “Such behavior is at the pinnacle of irresponsibility and is intentionally reckless.”

One of the lawyers, Mark Zaid, told CBS News on Sunday that he offered to have Republicans on the House Intelligence Committee submit questions to their client. The offer, which comes amid GOP complaints of unfair due process in the impeachment inquiry, would allow Republicans to directly question the whistleblower without going through the Democratic-controlled committee.

Trump labeled the impeachment inquiry a “scam,” again claiming on Sunday that the whistleblower report was inaccurate — “My phone call was ‘perfecto,’” he told reporters — and that the chairman of the House Intelligence Committee, Rep. Adam Schiff (D-Calif.), had lied to Congress and the American people.

He also said journalists would be doing the public a service in revealing the whistleblower’s name, tweeting later that afternoon: “The Fake News Media is working hard so that information about the Whistleblower’s identity, which may be very bad for them and their Democrat partners, never reaches the Public.”

Earlier in the day, the No. 3 Democrat in the House promised more openness about the impeachment investigation after weeks of witness depositions behind closed doors.

“Starting this week, we are going to release these transcripts for people to see and read for themselves,” Rep. Jim Clyburn (D-S.C.), the majority whip, said on CNN’s “State of the Union.” “We will get to the bottom of this, and then we’ll be able to make a determination at that time whether or not something happened that was treasonous.”

Clyburn added the House would begin holding televised hearings in the next two weeks, signaling that Democratic investigators had secured enough evidence against Trump to proceed with a public rollout — even with the fate of certain witnesses’ testimony this week still uncertain.

The chairman of the House Foreign Affairs Committee, Rep. Eliot Engel (D-N.Y.), added that investigators planned to interview their final witnesses this week, in what could be the last closed-door hearings of the impeachment inquiry.

“Everything else is going to be public,” Engel told ABC’s “This Week” on Sunday.

“This week, we’ll have the last of the witnesses come in,” he said. “Then it will be released, the transcripts will be released. Everything is transparent.”

Rep. Jim Clyburn (D-S.C.), the majority whip. | Manuel Balce Ceneta/AP Photo

Rep. Jackie Speier (D-Calif.), who sits on the House Intelligence panel, said she expected all of the transcripts to be released within the next five days.

“They’re going to be very telling to the American people,” Speier said on CBS’ “Face the Nation.” “There is no question now whether there was a quid pro quo, and now the question the Republicans are trying to throw out is, ‘Well, was there corrupt intent?’”

The shift to releasing transcripts and holding blockbuster hearings will probably turn the month of November into the most critical point of the House’s probe — decision time for Democrats on whether they will vote to impeach the president.

Still, House Majority Leader Steny Hoyer would not commit his caucus to a timeline for public hearings.

“Time is not constraining us,” the Maryland Democrat said on “Face the Nation.” “The truth and the facts are constraining us. We are going to move as soon as the facts and the truth dictate that we have.”

“I don’t know what witnesses are going to come forward, what they’re going to say, what evidence will have to be pursued,” Hoyer added.

As they inch closer to a potential vote on impeachment, Democrats have pointed to new polling that shows a surge in public support, including among independent voters, for their caucus’ fast-moving investigation.

Fifty-three percent of people said they approved of Democrats’ inquiry, compared with 44 percent of people who disapproved, according to an NBC News/Wall Street Journal poll released Sunday. And in an ominous sign for the president, 49 percent of people said Trump should be impeached and removed from office — up from 43 percent in the same poll last month. That is the same percentage that supported the impeachment and removal of Trump in a Fox News poll also released Sunday.

“I have been watching the polls all over the country,” Clyburn said on CNN, adding that “a majority of [independents] seem to be in favor of moving forward, and certainly overwhelmingly Democrats.”

House Speaker Nancy Pelosi also referenced the polling in a “Dear Colleague” letter on Saturday night, noting that surveys had “shifted from 59/34 opposed to impeachment when the inquiry was officially announced to 49/47, not only for impeachment, but also removal from office.”

Even as Democrats prepare to go public, investigators continue to battle the White House behind the scenes for access to key witnesses, including a national security aide, Robert Blair — who participated in the July 25 call between Trump and the Ukrainian president — who has been blocked from appearing on Capitol Hill on Monday. Energy Secretary Rick Perry, who is leaving his position soon, also said on Friday that he wouldn’t testify , ignoring a congressional subpoena.

Most Democrats have returned to their districts this week for recess, though the caucus’ leading investigators will remain in Washington for several days of planned closed-door depositions. It is unclear, however, whether the witnesses will appear.

Democrats are also working to secure testimony from former national security adviser John Bolton, potentially a key player. Rep. Jim Himes (D-Conn.), a member of the House Intelligence Committee, said on Sunday he believed that Bolton had been subpoenaed.

Republicans, meanwhile, struggled to defend Trump on the substance of the allegations — whether there was a quid pro quo meant to exchange held-up military aid to Ukraine for dirt on the Bidens.

Rep. Steve Scalise (R-La.), the House minority whip, said Trump’s call with Zelensky “was not talking about the 2020 election or political opponents,” though the administration’s partial call record specifically shows that Trump brought up Hunter Biden.

“It was about what happened prior in 2016, corruption in Ukraine,” Scalise said on “This Week.” “The law requires the president to certify that a country, before they get foreign aid, is actually taking steps to root out corruption.”

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White House adviser Kellyanne Conway said she didn’t know whether the Trump administration held up military aid to leverage it for the investigation, and instead stressed that Ukraine had ultimately received the aid.

“I don’t know, but I know they got that aid,” Conway said on “State of the Union.” “Here’s what’s absolutely, unimpeachably true: Ukraine has that aid.”

The investigation’s determining whether there was indeed a withholding of U.S. aid in return for Ukrainian help didn’t appear to bother Trump, however.

“False stories are being reported that a few Republican Senators are saying that President Trump may have done a quid pro quo, but it doesn’t matter, there is nothing wrong with that, it is not an impeachable event,” he tweeted on Sunday night. “Perhaps so, but read the transcript, there is no quid pro quo!”

Conway did not answer questions about whether the White House would allow officials such as Bolton to testify.

“The president has every right to exert executive privilege for a number of administration officials, current or former,” Conway said when asked about Bolton. “We as a White House will continue to exert executive privilege where we feel it is necessary.”

Several officials have defied the administration’s directive not to testify, however, sometimes with potentially damaging effect. That has led the president to question their credibility and their motives.

Of the many people who listened to his calls, Trump said on Sunday, “very few people that I know came forward. And they only came forward when you asked. And some of them are ‘Never Trumpers.’”