That raises a key question: What happens next?
The latest case involves Deputy National Security Adviser Charles Kupperman, who failed to appear for his deposition on Monday after being subpoenaed by impeachment investigators.
On Saturday, House Democrats sent a letter to Kupperman who last week asked a judge to decide whether he should obey the White House or Congress.
The letter from Reps. Adam Schiff, the Intelligence Committee chairman, Eliot Engel, the Foreign Affairs Committee chairman, and Carolyn Maloney, the acting chairwoman of the Oversight Committee, said that if Kupperman didn't appear, “his absence will constitute evidence that may be used against him in a contempt proceeding.”
On Monday, after Kupperman failed to show up, Schiff told reporters that "are not going to allow the White House to engage us in a lengthy game of rope-a-dope in the courts," adding that the White House's move to try and block officials from testifying could be used as evidence of obstruction of justice in potential articles of impeachment.
Congressional committees have yet to act against Trump administration officials who aren’t complying with subpoenas, but there are several options that Congress could take if members want to escalate the battle between the two branches.
Margaret Taylor, a fellow at the Brookings Institution and senior editor at the national security and legal blog Lawfare, called the executive branch’s stonewalling of Congress’ inquiry “really extraordinary.”
“It’s not politics as usual, it’s not how these things are traditionally played out and I think it’s quite worrying and troublesome for the integrity of our constitutional democracy that there’s not some amount of … recognition and accommodation by the executive branch of the legitimate prerogatives of the legislative branch,” Taylor said.
According to a Congressional Research Service Report, “Congress currently relies on two formal legal mechanisms to enforce subpoenas: criminal contempt of Congress and civil enforcement of subpoenas in the federal courts.”
The report, titled “Congressional Subpoenas: Enforcing Executive Branch Compliance,” said that criminal contempt statute can lead to “criminal punishment of the witness in the form of incarceration, a fine, or both.”
However, the report states that since this option is considered “punitive,” its used “mainly as a deterrent.”
“In other words, while the threat of criminal contempt can be used as leverage to encourage compliance with a specific request, a conviction does not necessarily lead to release of the information to Congress,” the report said.
Taylor also noted that its generally the executive branch that decides about the enforcement of criminal law.
“If your executive branch is telling you not to testify, then they’re not going to be punishing you criminally,” Taylor said.
Congress also has the option to file a lawsuit in federal district court as part of a process called “civil enforcement,” the report said.
This route calls on the courts to try and force an individual to comply, however, this option could take a long time to be adjudicated.
“It’s very time consuming, it doesn’t always result in a timely judgement so that’s sort of one avenue,” Taylor said.
Congress also has a third option on how to enforce its power using what’s called “inherent contempt power,” Taylor said.
“This is this idea that the congress pursuant to its constitutional authorities can essentially send out the sergeant at arms and detain people,” she explained.
Although this is something that could technically happen, and has happened historically, Taylor said, “it’s just not a feature of our current ... democracy right now.”
“I view it as like a very aggressive type of move that I don’t, I personally think Americans are not quite ready for,” she added.
According to Taylor, fines have also been explored as a way to enforce the inherent contempt power, but she said “there’s no precedent for it as far as I’m aware.”
"There's a lot to be worked out in terms of like, logistically how'd you do it, how you would sort of pass muster on sort of due process, it's again, uncharted territory," she said. "I think it probably could be done pursuant to the Congress' inherent contempt power.''
ABC News' Benjamin Siegel contributed to this report.