(CNN) House investigators, bracing for more witnesses to defy their demands at the behest of the White House, are now signaling they are prepared to begin the next phase of their impeachment inquiry even if their subpoenas are ignored across the board.

Democrats have teed up an ambitious schedule next week and are eager to secure the testimony of former national security adviser John Bolton , who was concerned about the push for Ukraine to investigate President Donald Trump's political rivals at a time when vital aid to the country had been held up by the White House , according to sworn testimony from key witnesses.

But the testimony of Bolton and at least 10 other key witnesses is far from assured, forcing Democrats to make a decision: Fight to secure testimony that could add more evidence to their case and will take time to play out, or urgently take the matter to the public as they begin their historic pursuit to potentially make Trump just the third President in history to get impeached.

A number of House Democrats told CNN that it's time for that next step, saying they've already built enough evidence to advance the proceedings to the public stage.

"This isn't an Agatha Christie novel — this is a shakedown," said Rep. Jamie Raskin, a Democrat from Maryland who has taken part in the closed-door depositions. "I think we have established an overwhelming case. But we have got very careful prosecutors on the staff who rightfully want to leave no witness unexamined, and they want every detail to be nailed down as much as possible. That's good."

Raskin added: "But at a certain point we have to say ... there's just been an overwhelming case that high crimes and misdemeanors have likely been committed against our country."

Besides Bolton, Democrats have scheduled interviews with eight other witnesses to speak to the events surrounding Trump's push for Ukraine to investigate the Bidens , the efforts to prevent a transcript of Trump's now-infamous July phone call with Ukraine's President Volodymyr Zelensky from being released, and the decision to delay nearly $400 million in security aid to Ukraine while holding up a bilateral meeting in Washington sought by Zelensky.

Earlier this week, Bolton's attorney Charles Cooper said his client would not appear voluntarily and was willing to receive a subpoena, though he made no commitments about complying.

But Cooper's other client is Bolton's deputy, Charles Kupperman, who defied a subpoena on Monday after filing a lawsuit saying he wanted a judge to rule whether he should comply with the subpoena or listen to the White House, which says he has immunity from testifying.

Cooper was coy in court on Thursday about Bolton's intentions, declining to respond to a judge's question about whether Bolton planned to sue like Kupperman had.

The court isn't likely to resolve questions about Kupperman's lawsuit until at least mid-December, meaning that if Bolton were to go to court, he too would be in limbo for more than a month and not appearing before the House.

The timeline could complicate the push by Democrats to conclude impeachment proceedings by the end of the year. But top Democrats are signaling they won't let court fights stand in the way of a timely conclusion to their probe.

In an interview on CNN, House Intelligence Chairman Adam Schiff conceded that the White House may succeed in blocking some witnesses from testifying, while arguing they would use the stonewalling as evidence of obstruction of Congress, a potential article of impeachment.

"The whole goal is to stall long enough to avoid doing their duty," Schiff, a Democrat from California, told CNN's Chris Cuomo. "They may prevent some of these witnesses from testifying and prevent the American people from learning the full facts around the President's misconduct, but even as they do that, they will be building a case against the President for obstructing the constitutional duties of Congress."

Transcripts could be released soon

The House is out of session next week when the block of depositions are scheduled, but once lawmakers return they'll have two weeks in November where public hearings could begin before Thanksgiving. House Speaker Nancy Pelosi said Friday that she believes hearings are possible this month.

"I would assume there would be public hearings in November," Pelosi said in a roundtable with Bloomberg News reporters and editors.

The House Intelligence Committee, which will conduct those public hearings, is also preparing for the release as early as next week of the closed-door deposition transcripts, Schiff said Thursday, as Democrats move toward making their case to the public.

Republicans are also eager to move into the next stage of the investigation where transcripts are released. One of the grievances GOP lawmakers have raised is that the transcripts aren't being made public quickly enough.

"We've heard from President Trump and President Zelensky, we've heard from Ambassador Volker, this idea that there was some kind of linkage or quid pro quo is just not there," said Rep. Jim Jordan of Ohio, the top Republican on the House Oversight Committee.

It's possible that the House committees leading the investigation — Intelligence, Foreign Affairs and Oversight — could continue to hold closed-door depositions even after they begin public hearings.

But Schiff has also said that one reason he hasn't yet released transcripts, as Republicans have demanded, is so witnesses can't use them to align their stories.

Bolton's appearance still unclear

If any depositions do take place next week, they could lead to additional Trump administration officials being called to testify, should new information be uncovered.

Schiff and Pelosi have been careful not to put a timeline on the investigation because Democrats have expanded their pool of witnesses as the probe has expanded from Trump's phone call with Zelensky to a broad, months-long campaign to push Ukraine to announce investigations into Vice President Joe Biden, Burisma -- the company that hired Biden's son Hunter -- and the 2016 election.

Democrats say they already have a trove of evidence showing that Trump conditioned US aid to Ukraine and a one-on-one meeting with Zelensky to the announcement of an investigation.

For instance, Bill Taylor , the top US diplomat to Ukraine, took meticulous notes documenting how he was told that the aid and a meeting were conditioned on the investigations. National Security Council Ukraine expert Lt. Col. Alexander Vindman , who listened in to the July 25 Trump-Zelensky call, raised concerns to NSC lawyers about what took place.

Democrats also have the text messages where Sondland, Volker, Giuliani and a top Zelensky aide discuss announcing the opening of an investigation and how it would be part of the July call.

And while Morrison provided the GOP argument a boost by saying he saw nothing wrong with the July call, he still corroborated Taylor's account about the aid and the investigations being linked.

This upcoming week, Democrats have scheduled depositions across the government, including National Security Council lawyers, the acting director of the Office of Management and Budget, and Energy Secretary Rick Perry.

The last deposition scheduled for the week is Bolton, who is the biggest wild card.

Democrats and Republicans acknowledge they still don't know at this point who will show up this week, but say the calendar suggests that attendance will be far from perfect.

On Monday there are four depositions scheduled: White House aide Rob Blair, National Security Council lawyer John Eisenberg, his deputy Michael Ellis and former Perry aide Brian McCormack, who is now at OMB. On Friday both Eisenberg and McCormack were subpoenaed, according to a source familiar with the matter.

Tuesday, OMB Deputy Director Michael Duffey has been subpoenaed to appear, and Wells Griffith, a White House aide at the National Security Council who works on energy and climate issues, has also been asked to testify. Both acting OMB Director Russ Vought and State Department counselor Ulrich Brechbuhl have received subpoenas to testify Wednesday, and Perry and State Department official David Hale have been asked to appear.

A Perry spokesperson said the secretary "will not partake in a secret star chamber inquisition" but that he would consider participating in an open hearing.

Schiff has not yet said whether he will issue a subpoena for Bolton, who is scheduled to appear on Thursday, though Democrats believe that is almost certain to occur.

"I'm not going to speak to any specifics but all I can say is there's no doubt that he has very relevant testimony in an impeachment inquiry," Schiff said Thursday. "The only question is whether he's going to be willing to come forward."