Democratic leaders still view the end of 2019 as a rough deadline to complete the impeachment process, and have started to talk privately about the topline logistics of moving the investigation into a public forum. But the unexpected deluge of testimony that investigators have received in private from witnesses willing to defy the White House’s efforts to silence them has left lawmakers reluctant to stanch the flow — and possibly miss crucial details.

“There has not been some date picked that we’re not telling you,” Rep. Sean Patrick Maloney (D-N.Y.), a member of the House Intelligence Committee, said in an interview.

“The concern that the chairman has, that I share, is that we do a thorough job because it’s really important that we get it right. And you’ve got to balance that with being quick,” Maloney added of the impeachment inquiry, which is examining Trump’s efforts to pressure Ukraine’s leaders to launch investigations of his political rivals in exchange for releasing military aid.

Schiff, whose panel is leading the impeachment investigation, told a meeting of House leaders this week that he hoped to expedite the closed-door process by occasionally holding two witness depositions per day.

Schiff underscored the need for a public aspect to the investigation, according to attendees, but he did not lay out a time frame to complete the private depositions. The California Democrat has already assured colleagues that the House intends to make the transcripts of its witness interviews public.

“We also anticipate that at an appropriate point in the investigation, we will be taking witness testimony in public, so that the full Congress and the American people can hear their testimony firsthand,” Schiff said in an Oct. 16 letter to House members.

Democratic leaders have defended the secrecy of the evidence-gathering process, arguing it prevents witnesses from coordinating their testimony and permits more thorough questioning of witnesses by professional lawyers of both parties — who typically are not permitted to ask questions in public sessions. They’ve also pointed out that Republicans who serve on the three panels leading the inquiry have the same access to the closed-door interviews as Democrats.

“Every member has a right to ask questions, and time is equally divided between the two parties. I don't know where they're getting this secrecy stuff,” House Majority Leader Steny Hoyer (D-Md.) said.

Though Democrats acknowledge the pressure Republicans are putting on them to open the inquiry to the public, Wednesday’s GOP-led storming of the secure facility where impeachment depositions are being conducted was never going to change the House’s path, they said.

“We’re not going to allow a stupid stunt to affect our approach to what needs to be a thorough inquiry,” said Rep. Tom Malinowski (D-N.J.), a Foreign Affairs Committee member. “We're going to hear from the people we need to hear from and then we'll move to public areas.”

Democrats have long acknowledged the competing pressures they face to be both thorough and rapid — to capitalize on a political climate for impeachment that has suddenly shifted in their favor, and to wrap up the process before the 2020 presidential primaries begin. So far, rank-and-file Democrats have largely been kept in the dark about House leaders’ intentions.

“We’re operating in the shadow, also, of a political calendar,” said Rep. Jamie Raskin (D-Md.), who sits on the Oversight and Reform Committee. “We would like to deal with all of this before we get into the voting next year.”

Lawmakers and aides say there has been very little discussion, even at leadership meetings, about another complicated aspect of the impeachment process: how the public impeachment proceedings would work. Democrats have not settled on a list of witnesses they would like to call publicly or on procedures that would allow Trump and Republicans to summon their own witnesses and cross-examine others.

Several lawmakers have said they want to see William Taylor — the top American diplomat in Kyiv whose damaging testimony earlier this week directly tied Trump to the Ukraine controversy — appear before the cameras.

Through Taylor and other witnesses, impeachment investigators have unearthed evidence that Trump used the nation’s military and diplomatic power as leverage to pressure Ukraine to investigate his political adversaries, including former Vice President Joe Biden.

Democrats say the evidence to support this allegation is already overwhelming: Trump himself provided a summary of his July 25 phone call with Ukrainian President Volodymyr Zelensky in which he pressed Zelensky to investigate spurious allegations against Biden. He also pushed Ukraine to probe a debunked theory that Ukraine, rather than Russia, hacked a Democratic Party server in 2016.

Democrats also obtained text messages between ambassadors who oversaw Ukraine policy. The messages raised concerns that Trump was withholding military aid to Ukraine and refusing a White House meeting with Zelensky in order to bend the newly elected leader to his will — even as Ukraine desperately needed the aid to fend off Russian aggression from its east.

Trump himself has publicly called on Ukraine and China to investigate Biden, and his acting chief of staff, Mick Mulvaney, recently acknowledged that military aid to Ukraine was conditioned in part on whether the European ally agreed to Trump’s demands. Mulvaney later walked the statement back.

There are several other unknowns, including how many articles of impeachment the House intends to consider. Democrats expect that when the Ukraine investigation is concluded, its findings will be passed on to the Judiciary Committee to craft articles. But there has been no determination yet as to when that transition would occur — to the private frustration of some Democrats who serve on the panel.

Lawmakers seem intent on drafting articles for “abuse of power” and “obstruction of Congress,” both of which can serve as catchalls for various allegations against the president. But there is still internal debate on whether to consider former special counsel Robert Mueller’s findings, in addition to evidence that Trump has benefited from foreign government spending at his properties.

Republicans have griped for weeks that the majority of their 197 members have been shut out of the impeachment process so far, and those that are permitted to review transcripts say they have been closely monitored by Democrats. Rep. Mark Meadows (R-N.C.), who has sat in on most depositions, said he is still hopeful Democrats will call some of the GOP’s preferred witnesses.

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Georgia Rep. Doug Collins, the top Republican on the House Judiciary Committee, has argued that Democrats are violating House rules by depriving members of access to the material collected by the committees running the impeachment process. He specifically cites House Rule XI, which indicates "all committee records (including hearings, data, charts, and files) ... shall be the property of the House, and each Member, Delegate, and the Resident Commissioner shall have access thereto.”

Collins has written to Schiff and other committee leaders, asking them to prepare materials for him to review — but a person familiar with the request says the committees have not replied.

Democrats maintain that they are following standard procedures similar to the early stages of impeachment proceedings against Presidents Bill Clinton and Richard M. Nixon. And, as members of the three committees leading the probe, nearly a quarter of the House Republican Conference can sit in on the depositions.

Rep. Dean Phillips of Minnesota, a swing-district Democrat who has sat in on several of the depositions, said the GOP’s complaints about secrecy won’t speed up the timeline to finish closed-door investigations — but he acknowledged the importance of a public airing of allegations against the president.

“I understand why people say, more transparency, more in the public. I totally understand,” Phillips said. “The transcripts should be released to the public. The hearings should be conducted publicly, and certainly, the trial, should be fully publicly, as it will be.”

Sarah Ferris contributed to this report.