Acting White House chief of staff Mick Mulvaney is facing a storm of criticism from former and current White House officials for his handling of the impeachment inquiry, his leadership of the White House staff, and communications overall. A former high-ranking aide, who would only speak on background, called Mulvaney a "mess." In this person's view, Mulvaney, rather than aggressively protecting the president from people and situations that could pose a danger to his ability to govern, took a more passive role, standing off to the side carrying out the president's wishes, in an effort not to rock the West Wing boat.

After congressional Republicans and former top White House officials said they were unhappy about how the White House was handling the impeachment inquiry, the White House recognized a need for more coherent messaging, and it seemed as though efforts to address the problem were underway with the announcement that former Congressman Trey Gowdy would be joining the legal team. Trump attorney Jay Sekulow released a statement Wednesday night saying that Gowdy's "legal skills and advocacy will serve the president well."

But the next day, as President Trump was leaving for a rally in Minneapolis, he told reporters, "Trey Gowdy is a terrific guy. I think there's a problem with — he can't start for another couple of months because of lobbying rules and regulations."

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The White House had hoped that Gowdy, who presided over the Benghazi hearings targeting Hillary Clinton, would be an effective and serious advocate on the president's behalf. Insiders worried about the effect of Trump personal attorney Rudy Giuliani's investigative freelancing and television appearances that might damage the president's case.

According to a source close to the process, Mulvaney had spoken with Gowdy about coming onboard as a White House employee, but Gowdy did not want to leave his life as a civilian. The two settled on making him an outside counsel instead. Gowdy met with Mr. Trump, Vice President Pence, Jared Kushner and Mulvaney for lunch, and the group discussed impeachment strategy. Mr. Trump had another conversation with Gowdy before Sekulow issued the statement welcoming Gowdy aboard.

Gowdy had been outside counsel for two days before he flagged a congressional lobbying statute that might prevent him from appearing on television on the president's behalf. CBS News confirmed a New York Times report that noted that the law firm that currently employs Gowdy, Nelson Mullins, also had restrictions that would apply.

Mulvaney dismissed the concerns about the lobbying restrictions, convinced that they could be overcome. But that was not the case, and the president himself ended up admitting that Gowdy would not be able to join his legal team for now. Sekulow and White House counsel Pat Cipollone had also signed off on Gowdy's hiring, in addition to Mulvaney. Still, it's been Mulvaney who's borne most of the blame for this latest misstep.

From the outset of the impeachment inquiry, the administration has declared it would not cooperate with the investigation because House Speaker Nancy Pelosi has not held a floor vote on the matter. But any efforts the White House has made to stop current or former officials from testifying have fallen short, and they do not appear to have had much success in limiting testimony.

The congressional committees carrying out the inquiry have heard from the former special envoy to Ukraine, Kurt Volker; the ousted ambassador to Ukraine, Marie Yovanovitch, who still works for the State Department; Fiona Hill, the president's former Russia adviser; and George Kent, a career State Department official who is an expert on Ukraine. All of them have reportedly testified about Giuliani's involvement in Ukraine policy, despite the fact that he is not a government official.

"The knives are out for Mulvaney," one former top White House official told CBS News. The former aide compared this moment in Mulvaney's tenure to the days when his predecessor John Kelly had lost the confidence of the president, which allowed for dissension among the White House ranks to spread.

So far, there has been no indication that the president is unhappy with his acting chief of staff, though there are plenty of complaints about how Mulvaney is managing the White House.

"Mulvaney has allowed Jared (Kushner) and Ivanka (Trump) to run the place," said the former longtime senior official, who served in the White House when Reince Priebus and John Kelly each had the job. The official compared the current White House to the "Game of Thrones" days of the Priebus era, which seemed to be characterized by infighting, backstabbing and a collective lack of focus.

"There is no structure. There is just chaos," the former aide said of Mulvaney's management. It's a departure from Kelly, who tried to maintain some degree of discipline. Now, the aide says, the staff has reverted back to the disarray of the early days of the Trump administration.

This is apparent in the way the impeachment inquiry is being addressed, according to the former Trump aide, who says many in Mr. Trump's orbit fear the White House has allowed the Democrats to set the narrative early on and fumbled the counter-message. They worry that this scenario has spiraled from what could have been just a bad story into an impeachment inquiry that jeopardizes Mr. Trump's presidency.

This week, Mulvaney's name emerged in the inquiry itself. The New York Times reported Monday that Mr. Trump's former Russia adviser, Fiona Hill, testifed to Congress that Mulvaney worked with the president's personal lawyer, Rudy Giuliani, on a rogue operation involving Ukraine that had legal implications. Their dealings prompted then-national security adviser John Bolton to instruct Hill to inform National Security Council lawyers.

"I am not part of whatever drug deal Rudy and Mulvaney are cooking up," Bolton told Hill to convey to the lawyers, the Times reported about her testimony.

The policymaking process in the West Wing is also disorganized, current and former White House officials told CBS News.

It's a departure from the style of former chief of staff John Kelly, who instituted a rigorous and often time-consuming policymaking apparatus that included coordination among agencies, consultation with stakeholders, a review by White House lawyers, and other steps before a policy reached the president's desk for approval.

There is less emphasis on those protocols under Mulvaney. Current and former officials say staffers go directly to Mulvaney to ask for a meeting with Mr. Trump. This has led to meetings in which presidential decisions are made without the appropriate personnel present and at times incomplete policy work.

A current White House official lamented that the lapse in protocols has made the West Wing messy and inefficient, rife with competing factions and flagging morale.

Acting chief of staff "Mick (Mulvaney) isn't a process person," the current staffer said. "You go in and get a decision. Someone else will go in and get a different decision," which further delays the process, the source said.

"The White House is totally unmanaged right now...There's just no coordinated way of figuring out what's happening," the staffer said.

The source was provided anonymity to speak candidly about internal dynamics at the White House. A longtime aide and administration source close to Mulvaney declined comment, and a White House source in Mulvaney's office did not respond to requests for comment.

The White House press office disputed the premise of disorder in the West Wing, but declined to provide further comment.

A few months after he was named acting chief of staff, Mulvaney made it clear that he'd do the job differently than his predecessor and said he thought that Kelly's style wasn't the right fit for this president.

"That's not Donald Trump, and that's not the Donald Trump White House," he told CBS News' Major Garrett on "The Takeout" podcast in May. "So, while that militaristic sort of approach was necessary to sort of get things back on track after the first couple of months of the administration, it wasn't the right long term plan."

Now, the president no longer receives the wide range of information, meetings with stakeholders and policy briefs that Kelly regularly gave him, current and former officials say. Mr. Trump is no longer inundated by facts before he makes decisions. The president tired of Kelly's approach, and Mulvaney has made a virtue of not being like Kelly or appearing in any way to manage the president.

Despite the concerns of these current and former White House officials, amid mounting questions about Mr. Trump's handling of Ukraine and his sudden decisions on U.S. troop movement in Syria, there has been no indication from President Trump that he is unhappy with his acting chief of staff.

Major Garrett, Jenna Gibson and Sara Cook contributed to this report.