Asked by a reporter if there was a quid pro quo on Ukraine, Mulvaney appeared to confirm there was one.

"We do that all the time with foreign policy," Mulvaney said at a news conference last month, adding, "And I have news for everybody. Get over it. There is going to be political influence in foreign policy.

As Trump and his allies pursued the investigations, Mulvaney appeared to come under fire from within the West Wing as well.

Trump’s former top Russia aide Fiona Hill testified to impeachment investigators that former National Security Adviser John Bolton said to her, “I am not part of whatever drug deal Sondland and Mulvaney are cooking up,” a reference to Gordon Sondland, the U.S. ambassador to the European Union.

Several Mulvaney aides have refused to appear for depositions in recent days as Democrats have reached closer to the Oval Office in their inquiry.

Michael Duffey, OMB's national security chief, and Wells Griffith, the senior director for international energy and environment at the NSC, did not appear Tuesday for their scheduled testimony.

And White House legislative director Eric Ueland on Tuesday signaled Mulvaney was unlikely to appear for the Nov. 8 deposition.

"I think we made our position pretty clear on who's attending and not attending these spurious, made-up requests for folks to show up," he told reporters.

Andrew Desiderio and Marianne LeVine contributed to this report.