In a shambolic press conference with the Russian president on Tuesday, Mr Trump dismissed claims Russia interfered in the 2016 US presidential elections.
He has since invited Putin to the White House, provoking widespread disbelief.
Now White House sources say staff are “depressed” and eager to make their escape.
One Republican told Politico: “Nobody wants to take on the public heat of resigning right now, but there are a bunch of people who were thinking maybe they’d leave after the midterms who are very seriously starting to consider accelerating their timetable.”
Yesterday it was revealed three of the top cybersecurity officials at the Federal Bureau of Investigation (FBI) are retiring.
FBI sources say morale is low after attacks from President Trump for their handling of investigations into Russian election meddling.
Mr Trump contradicted the intelligence services at this week’s news conference in Helsinki by saying he didn’t see any reason why election meddling in 2016 would be Russia.
In an astonishing u-turn, the president later claimed he misspoke and meant to say he didn’t see any reason why the meddling “wouldn’t” be Russia.
The Ex-CIA chief John Brennan called Trump’s words “nothing short of treasonous.”
He added: “This I think rises to the point of good American patriots resigning in objection to that performance by Donald Trump.”
Yesterday the White House revealed on Twitter that Putin has been invited to Washington.
US intelligence chief Dan Coats was informed live on television, and said after a shocked pause: “That’s going to be special”.
The former director of national intelligence, James Clapper said, if he were Coats he “would resign in a heartbeat”.
Although high turnover in stressful White House jobs is common, Trump’s administration has had the highest first-year turnover in the last 40 years with a rate of 34%, twice that of Ronald Reagan’s administration.
In Michael Wolf’s tell-all book The Fire and the Fury Trump is described as “an idiot surrounded by clowns.”