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President Donald Trump’s former deputy national security adviser Charles Kupperman defied a congressional subpoena Monday, failing to appear for a closed-door deposition before House impeachment investigators and throwing a new hurdle into Democrats’ plans to quickly gather evidence in their inquiry.

But Democrats said that attempts by Kupperman and others not to comply with subpoenas will not delay their impeachment investigation, regardless of whether they decide to go to court to try to enforce the subpoenas.

“We are not willing to allow the White House to engage us in a lengthy game of rope-a-dope in the courts,” House Intelligence Chairman Adam Schiff said Monday after Kupperman did not appear.

Schiff said that he was confident the House would ultimately prevail in court, though he did not say whether the House would pursue that route — given that any court process is likely to take weeks, if not months, to resolve.

“We expect that the court will make short shrift of that argument, but nonetheless, we move forward,” Schiff said.

Kupperman threw a new wrench into the Democratic impeachment investigation on Friday when he filed a lawsuit asking a judge to rule whether he had to comply with the House subpoena, pointing to the White House’s stance that the impeachment inquiry is illegitimate. Kupperman’s attorney, Charles Cooper, argued that his client was caught between competing demands between the Executive and Legislative branches and needed the courts to rule before Kupperman would testify.

The chairs of the three committees leading the House impeachment inquiry rejected Kupperman’s lawsuit, threatening him with contempt if he did not appear. The Democrats wrote in a letter Saturday that the suit was “an obvious and desperate tactic by the President to delay and obstruct the lawful constitutional functions of Congress and conceal evidence about his conduct from the impeachment inquiry.”

Cooper responded with a letter Sunday arguing it was not Kupperman who is contesting the validity of the subpoena but the President.

“If your clients’ position on the merits of this issue is correct, it will prevail in court, and Dr. Kupperman, I assure you again, will comply with the Court’s judgement,” Cooper wrote in a letter to the House Intelligence Committee.

Democrats would like to speak to Kupperman, who was listening to the July 25 call between Trump and Ukrainian President Volodymyr Zelensky in which Trump pushed Ukraine to investigate his political opponents. But his suit looms over another more senior witness Democrats are eager to speak with: former national security adviser John Bolton.

Bolton, who was Kupperman’s boss on the National Security Council, has also hired Cooper as an attorney.

Schiff, a California Democrat, said on ABC’s “This Week” on Sunday that he expects similar resistance from Bolton.

“We will be doing public hearings and I think we’ll being doing them soon,” Schiff said. “I don’t want to give precise timing because in part we’re struggling with the White House’s continuing efforts to obstruct our investigation, to obstruct witnesses coming in. My guess is they’re going to fight us having John Bolton in, for example.”

Asked about Kupperman’s decision not to testify Monday, Ohio Rep. Jim Jordan, the top Republican in the House Oversight Committee, pointed to the letter from Kupperman’s attorney stating he was willing to come if a court ruled the subpoena was legitimate, though Jordan himself argued that the probe was “a charade.”

“This is not an investigation,” said Rep. Mark Meadows, a North Carolina Republican. “These are a few depositions designed to get an outcome that was predetermined.”

While Democrats have been successful fighting the Trump administration in courts thus far — a judge ruled Friday that the impeachment inquiry was valid — trying to force Kupperman or Bolton to testify through contempt or in the courts poses a key problem for Democrats: It’s likely to take weeks, if not months, for them to prevail.

Schiff and other Democrats have said previously that witnesses and agencies who defy subpoenas for documents and testify are obstructing Congress, which could be cited in articles of impeachment. But Kupperman is the first impeachment witness who has been threatened with contempt for not appearing.

Democrats’ impeachment timeline is already slipping past what some lawmakers had initially predicted, and a court battle to obtain witness testimony could push it into 2020 — and into the presidential election calendar.

There are five additional witnesses scheduled to appear behind closed doors for depositions this week, including Tim Morrison, an official on the National Security Council who was cited repeatedly in US diplomat Bill Taylor’s testimony. Three more officials, who have fought testifying voluntarily, were subpoenaed to appear next week.

This story has been updated with additional developments Monday.

CNN’s Zach Cohen, Suzanne Malveaux and Jake Lubbehusen contributed to this report.