Washington CNN  — 

President Donald Trump on Tuesday dismissed the escalating impeachment inquiry on Capitol Hill during a jovial Rose Garden appearance, but sources say there is mounting frustration over the cavalcade of administration witnesses providing testimony.

“I wouldn’t worry about it, fellas, I wouldn’t worry about it,” Trump joked alongside Stanley Cup champions the St. Louis Blues.

Inside the West Wing, sources say, there is escalating concern about administration witnesses who are giving depositions on Capitol Hill.

The frustration comes as the Office of the Vice President said it will not comply with House requests for documents related to the impeachment inquiry, according to a Tuesday letter from Matthew Morgan, counsel for Vice President Mike Pence.

The letter cited White House counsel’s previous letter to House Speaker Nancy Pelosi questioning the legitimacy of the impeachment inquiry, saying the process “calls into question your commitment to fundamental fairness and due process rights.”

“Instead of being accountable to the American people and casting a vote to authorize what all agree is a substantial constitutional step, you have instead attempted to avoid this fundamental requirement by invoking the Speaker’s announcement of an ‘official impeachment inquiry’ at a press conference?” Morgan wrote in a letter to House Oversight Chairman Elijah Cummings, House Foreign Affairs Chairman Eliot Engel, and House Intelligence Chairman Adam Schiff.

Morgan added, “Never before in history has the Speaker of the House attempted to launch an ‘impeachment inquiry’ against a President without a majority of the House of Representatives voting to authorize a constitutionally acceptable process.”

Also on Tuesday, George Kent, the State Department official in charge of Ukraine policy, was the latest witness to be questioned. Fiona Hill, Trump’s former Russia adviser, sat down for more than 10 hours on Monday.

Watching this, officials are growing frustrated because they are mainly being forced to learn about what these officials divulged from news reporters. There is no White House counsel present in the room and officials are not given transcripts or readouts after they leave, one person told CNN.

The White House sent an eight-page letter declaring war on the inquiry by deeming it unconstitutional – but officials have been unable so far to prevent officials from complying with requests and subpoenas.

Some key players and agencies have rejected House Democrats’ subpoenas, including Trump’s personal attorney Rudy Giuliani and the Office of Management and Budget.

This story has been updated with additional developments Tuesday.

CNN’s Michael Warren and Sara Murray contributed to this report.